This section has 2 verses.
 
Titus 3:1-2
1 Put them in mind to be subject to principalities and powers, to obey magistrates, to be ready to every good work,
2 To speak evil of no man, to be no brawlers, but gentle, shewing all meekness unto all men.
 
 We will begin with the Barclay commentary.

CHRISTIAN CITIZENS

First, the paraphrase of verses 1 and 2:

Remind them to be duly subject to those who are in power and authority, to obey each several command, to be ready for every work so long as it is good, to slander no one, not to be aggressive, to be kindly, to show all gentleness to all men.

HERE is laid down the public duty of all Christians; and it is advice which was particularly relevant to the people of Crete. The Cretans were notoriously turbulent and quarrelsome and impatient of all authority. Polybius, the Greek historian, said of them that they were constantly involved in ‘insurrections, murders and internecine wars’. This passage lays down six qualifications for good citizens.

Good citizens are law-abiding. They recognize that, unless the laws are kept, life becomes chaos. They give a proper respect to those who are set in authority and carry out whatever command is given to them. Christianity does not insist that people should cease to be individuals, but it does insist that they remember that they are also members of a group. ‘Man’, said Aristotle, ‘is a political animal.’ That means that we best express our personalities not in isolated individualism but within the framework of the group.

Good citizens are active in service. They are ready for every work, as long as it is good. The characteristic modern disease is boredom, and boredom is the direct result of selfishness. As long as people live on the principle of ‘Why should I do it? Let someone else do it’, they are bound to be bored. The interest of life lies in service.

Good citizens are careful in speech. They must slander no one. We should never say about other people what we would not like them to say about us. Good citizens will be as careful of the words they speak as they are about their actions.

Good citizens are tolerant. They are not aggressive. The Greek word is amachos, which means not a fighter. This does not mean that good citizens will not stand up for the principles which they believe to be right, but that they will never be so opinionated as to believe that no other way than their own is right. They will allow to others the same right to have their own convictions as they claim for themselves.

Good citizens are kind. The word is epieike¯s, which describes someone who does not stand upon the letter of the law. Aristotle said of this word that it denotes ‘indulgent consideration of human infirmities’ and the ability ‘to consider not only the letter of the law, but also the mind and intention of the legislator’. Someone who is epieike¯s is always ready to avoid the injustice which often lies in being strictly just.

Good citizens are gentle. The word is praus, which describes the person whose temper is always under complete control. Such people know when to be angry and when not to be angry. They patiently bear wrongs done to them but are always ready to spring to the help of others who are wronged.

Qualities like these are possible only for those in whose hearts Christ reigns supreme. The welfare of any community depends on the acceptance by the Christians within it of the duty of demonstrating to the world the nobility of Christian citizenship. ~Barclay Commentary

Now to the other commentaries. We will begin with the general and go to the specific.

First with the Matthew Henry Main which covers verses 1-8. I am giving you what this commentary has to say about verse 2. The commentary is going through the duties of firstfruits. The first two from verse 1 are:

1] Put them in mind to be subject to principalities and powers, to obey magistrates.
2] To be ready for every good work.

The commentary proceeds into verse 2:

And, 3. To speak evil of no man: mēdena blasphēmein, to revile, or curse, or blaspheme none: or (as our translation more generally) to speak evil of none, unjustly and falsely, or unnecessarily, without call, and when it may do hurt but no good to the person himself or any other. If no good can be spoken, rather than speak evil unnecessarily, say nothing. We must never take pleasure in speaking ill of others, nor make the worst of any thing, but the best we can. We must not go up and down as tale-bearers, carrying ill-natured stories, to the prejudice of our neighbour's good name and the destruction of brotherly love. Misrepresentations, or insinuations of bad intentions, or of hypocrisy in what is done, things out of our reach or cognizance [kog-nuh-zuh ns] [knowledge; awareness] , these come within the reach of this prohibition. As this evil is too common, so it is of great malignity [muh-lig-ni-tee] [intense ill will]. If any man seemeth to be religious and bridleth not his tongue, that man's religion is vain, James 1:26. Such loose uncharitable talk is displeasing to God, and hurtful among men. Proverbs 17:9, He that covereth a transgression seeketh love (that is, to himself by this tenderness and charity, or rather to the transgressor); but he that repeateth a matter (that blazes and tells the faults of another abroad) separateth very friends; he raises dissensions and alienates his friend from himself, and perhaps from others. This is among the sins to be put off (Ephesians 4:31); for, if indulged, it unfits for Christians communion here and the society of the blessed in [The Kingdom], 1 Corinthians 6:10. Remind them therefore to avoid this.

Quoted verses:
James 1:26
If any man among you seem to be religious, and bridleth not his tongue, but deceiveth his own heart, this man's religion is vain.

Proverbs 17:9
He that covereth a transgression seeketh love; but he that repeateth a matter separateth very friends.

Ephesians 4:31
Let all bitterness, and wrath, and anger, and clamour, and evil speaking, be put away from you, with all malice:

1 Corinthians 6:10
Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God.

And, 4. To be no brawlers; amachous einai - no fighters, either with hand or tongue, no quarrelsome contentious persons, apt to give or return ill and provoking language. A holy contending there is for matters good and important, and in a manner suitable and becoming, not with wrath nor injurious violence. Christian must follow the things that are conducive to peace, and that in a peaceful, not a rough and boisterous and hurtful way, but as becomes the servants of the God of peace and love (Romans 12:19), Dearly beloved, avenge not yourselves, but rather give place unto wrath; this is the Christian's wisdom and duty. The glory of a man is to pass over a transgression; it is the duty of a reasonable, and therefore certainly of a Christian man, whose reason is improved and advanced by religion; such may not, and will not, presently fall foul on one who has offended him, but, like God, will be slow to anger, and ready to forgive. Contention and strife arise from men's lusts, and exorbitant unruly passions, which must be curbed and moderated, not indulged; and Christians need to be reminded of these things, that they do not by a wrathful contentious spirit and behaviour displease and dishonour God and discredit religion, promoting feuds in the places where they live. He that is slow to anger is better than the mighty, and he that ruleth his spirit than he that taketh a city.

Quoted verse:
Romans 12:19
Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.

Wherefore it follows, 5. But gentle; epieikeis, equitable and just, or candid and fair in constructions of things, not taking words or actions in the worst sense; and for peace sometimes yielding somewhat of strict right.

And, 6. Showing all meekness to all men. We must be of a mild disposition, and not only have meekness in our hearts, but show it in our speech and conduct. All meekness - meekness in all instances and occasions, not towards friends only, but to all men, though still with wisdom, as James admonishes, James 3:13. “Distinguish the person and the sin; pity the one and hate the other. Distinguish between sin and sin; look not on all alike, there are motes and beams. Distinguish also between sinner and sinner: of some have compassion, others save with fear, pulling them out of the fire, thus making a difference, Jude 1:22-23. Mind these things; the wisdom that is from above is pure and peaceable, gentle and easy to be entreated.” Meekness of spirit and demeanour renders religion amiable; it is a commanded imitation of Christ the grand exemplar, and what brings it own reward with it, in the ease and comfort of the disposition itself and the blessings accompanying it. These shall be glad and rejoice, shall be taught and guided in their way, and satisfied with bread, and beautified with salvation. ~Matthew Henry Main

Quoted verses:
James 3:13
Who is a wise man and endued with knowledge among you? let him shew out of a good conversation his works with meekness of wisdom.

Jude 1:22-23 ...a book about apostasy
22 And of some have compassion, making a difference:
23 And others save with fear, pulling them out of the fire; hating even the garment spotted by the flesh.

Now from the Matthew Henry Concise which covers verses 1-7.

Spiritual privileges do not make void or weaken, but confirm civil duties. Mere good words and good meanings are not enough without good works. They were not to be quarrelsome, but to show meekness on all occasions, not toward friends only, but to all men, though with wisdom, James 3:13. And let this text teach us how wrong it is for a Christian to be churlish [chur-lish] [boorish; rude; mean; difficult to work or deal with] to the worst, weakest, and most abject.

Quoted verse
James 3:13
Who is a wise man and endued with knowledge among you? let him shew out of a good conversation his works with meekness of wisdom.

The servants of sin have many masters, their lusts hurry them different ways; pride commands one thing, covetousness another. Thus they are hateful, deserving to be hated. It is the misery of sinners, that they hate one another; and it is the duty and happiness of saints to love one another. And we are delivered out of our miserable condition, only by the mercy and free grace of God, the merit and sufferings of Christ, and the working of his Spirit. God the Father is God our Saviour. He is the fountain from which the Holy Spirit flows, to teach, regenerate, and save his [sinful] creatures; and this blessing comes to mankind through Christ. The spring and rise of it, is the kindness and love of God to man. Love and grace have, through the Spirit, great power to change and turn the heart to God. Works must be in the saved, but are not among the causes of their salvation. A new principle of grace and holiness is wrought, which sways, and governs, and makes the man a new creature. Most pretend they would have [the Kingdom] at last, yet they care not for holiness now; they would have the end without the beginning. Here is the outward sign and seal thereof in baptism, called therefore the washing of regeneration. The work is inward and spiritual; this is outwardly signified and sealed in this ordinance. Slight not this outward sign and seal; yet rest not in the outward washing, but look to the answer of a good conscience, without which the outward washing will avail nothing. The worker therein is the Spirit of God; it is the renewing of the Holy [Spirit].

Through him we mortify sin, perform duty, walk in God's ways; all the working of the Divine life in us, and the fruits of righteousness without, are through this blessed and holy Spirit. The Spirit and his saving gifts and graces, come through Christ, as a Saviour, whose undertaking and work are to bring to grace and glory. Justification, in the gospel sense, is the free forgiveness of a sinner; accepting him as righteous through the righteousness of Christ received by faith. God, in justifying a sinner in the way of the gospel, is gracious to him, yet just to himself and his law. As forgiveness is through a perfect righteousness, and satisfaction is made to justice by Christ, it cannot be merited by the sinner himself. Eternal life is set before us in the promise; the Spirit works faith in us, and hope of that life; faith and hope bring it near, and fill with joy in expectation of it. ~Matthew Henry Concise with some editing by me

Here is an item from the Biblical Illustrator:

To speak evil of no man
On evil speaking
I. There are several, reasons for which Christians ought to be exhorted to refrain from evil speaking.
1. It is not only a mean and shameful, but a pernicious [per-nish-uh s] [hurtful]  fault; it produces much harm in society, and is a cause why many live hateful and hating one another, and die in the same unfriendly disposition.

2. It is a common and widespread fault, and few, very few, are entirely free from it. It is not confined to wicked and profane persons; it is to be found in some measure even in those who have their virtues, their good and useful, and amiable qualities and accomplishments, who live soberly and honestly, who love their friends and are active to serve and oblige them, who are not uncharitable to the poor, who have a sense of religion, and worship God both in public and in private.

3. They who are addicted to it, either seldom reflect upon its odious nature, or are not sensible when and how often they thus offend, or have several plausible though vain excuses to justify themselves.

II. Evil speaking consists in spreading reports to the disadvantage of our neighbour; and of this fault there are three distinct kinds or degrees.
1. The worst kind of it is to spread lies of our own invention concerning others.

2. The next is to report things to their disadvantage, of the truth of which we are not sufficiently assured.

3. The lowest degree is to say of them that evil which we know to be true.

III. There is no occasion to prove and expose the folly and dishonesty of the two former kinds. It would be losing time and words. I shall, therefore, chiefly discourse of the latter, and show how blamable even this is for the most part.
1. We should not be too forward to publish the faults of others, because it is no sufficient excuse for us, that what we say is true, and that they against whom we speak deserve such usage.

2. Another argument against censoriousness [sen-sawr-ee-uh s] [being severely critical] is contained in this plain precept of the gospel—“Whatsoever ye would that men should do unto you, do ye so unto them.”

3. We should not accustom ourselves to discourse about the faults of our neighbour, because it may betray us by degrees into a worse kind of evil speaking.

4. We should not be forward to expose the faults of others, because by so doing we may bring upon them a punishment too heavy for the offence.

5. We should be cautious how we censure others, because we may misrepresent them, and yet say nothing of them that is not true.

6. To disclose the faults and indiscretions of others is often very pernicious to society, raises infinite variances amongst men, and tends to destroy the slender remains of love and charity which subsist in the Christian world.

7. Since for the most part we cannot discern the exact nature and degree of other men’s faults, we may easily think too hardly and judge too severely of them. Their faults, when we know not the circumstances attending them, are like objects seen by us at a great distance, or at twilight: we see them neither in shape, nor in size or color, such as they really are.

8. That we may restrain ourselves from talking of the faults of others, we should also consider that such discourse is produced by bad causes, and proceeds from a corrupted heart; and that all good and wise persons who hear us will judge of us accordingly. Speech is the child of thought; and a child it is which greatly resembles its parent. When the discourse is censorious and malicious, the mind which conceives it is no better.

9. Besides, this is an offence which seldom escapes correction. If human laws cannot chastise it, except in some few cases, the persons who are ridiculed or censured will fully supply that defect.

10. Lastly, we should be cautious not to give way to this inclination, because if we be once accustomed to it there is no probability that we shall ever leave it off. Of all bad habits, those of the tongue are, perhaps, the hardest to be cured. The reason is this: We deceive ourselves in thinking that words can do little or no hurt, and that the guilt of them is inconsiderably small, and consequently we speak at random what comes uppermost. ~Biblical Illustrator

Now to one of the specific commentaries. This one the John Gill:

To speak evil of no man - As not of one another, so not of the men of the world, to the prejudice of their names and characters, which are tender things, and ought to be gently touched; nor of magistrates, principalities, and powers, of persons in dignity and authority, which the false teachers were not afraid to speak evil of, and by their principles and practices taught others to do the same:

To be no brawlers - or "fighters", either by blows or words; not litigious and quarrelsome, wrangling and striving about things to no profit, and to the detriment and disturbance of civil government, churches, neighbourhood, and families; which is very unbecoming the followers of Jesus, who strove not, nor cried, nor was his voice heard in the streets. But gentle, showing all meekness to all men; yielding and giving way, rather choosing to suffer wrong than to brawl, contend, and litigate a point; taking the advice of Christ in Matthew 5:39, carrying it in a meek and humble manner to men of all ranks and degrees, whether superior or inferior, rich or poor, bond or free, Jews or Gentiles, members of the church, or men of the world. ~John Gill

Quoted verse:
Matthew 5:39
But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also.

Notice the commentary on the phrase, "Turn to him the other also."
 

Turn to him the other also - That is, rather than avenge thyself, be ready to suffer patiently a repetition of the same injury. But these exhortations belong to those principally who are persecuted for righteousness’ sake. Let such leave the judgment of their cause to Him for whose sake they suffer. The Jews always thought that every outrage should be resented; and thus the spirit of hatred and strife was fostered. ~John Gill

So, let us see to our duties.  Speak no evil.  Do not be litigious, quarrelsome or striving about things to no profit.  Be peaceable, gentle and easy to be entreated.  These are the lessons of verse two.