What do the Saints say about "Talking about your self"?

Christ already gives us the guide on this. Matthew 6 says this:

“Beware of practicing your piety before others in order to be seen by them; for then you have no reward from your Father in heaven.

2 “So whenever you give alms, do not sound a trumpet before you, as the hypocrites do in the synagogues and in the streets, so that they may be praised by others. Truly I tell you, they have received their reward. 3 But when you give alms, do not let your left hand know what your right hand is doing, 4 so that your alms may be done in secret; and your Father who sees in secret will reward you.

5 “And whenever you pray, do not be like the hypocrites; for they love to stand and pray in the synagogues and at the street corners, so that they may be seen by others. Truly I tell you, they have received their reward. 6 But whenever you pray, go into your room and shut the door and pray to your Father who is in secret; and your Father who sees in secret will reward you. NRSVCE

Saint Paul also tells us that he is "chief of sinners" (1 Tim 1:15). And we can look at other saints who were models of humility. Saint Martin de Porres is a personal favorite. He exemplified Matt 6 perfectly. He would go and find a place to pray where others rarely went, and sometimes the brothers would stumble upon him praying there. But, he was trying to avoid being seen publicly praying. He also would heal the sick in town, and although some of his healings were miraculous, he would not accept praise for his holiness when people recognized it.

Saint Rose of Lima, too, would take on penances and hide them from others. She wore a makeshift crown of thorns concealed beneath her habit, for example.

Saint Augustine, famously, composed his autobiography under the title Confessions, wherein he laid bare all of his most egregious sins for the world. Rarely are autobiographies so honest in the shortcomings of their authors.

I think that practicing humility primarily entails following the commands in Matt 6. If you want to build that virtue, prayerfully discern penances for yourself (not necessarily those so extreme as St. Rose), give alms, and pray in secret. Don't let others know what you are doing. And, furthermore, you should interiorly assume that others are doing even more penances, almsgivings, and prayers than you are in secret. Be the first to admit to a fault and the last to defend yourself from personal attacks.

This is all far, far easier said than done.

The opposite of being humble is being proud. True humility is, indeed, reflected in speech but nobody can become humble by speaking humbly. If a person is not humble in heart, any speech that seems humble will not be at all, though others might think, "There goes a humble fellow!" It is the same with conduct. A person may conduct themselves in a manner that appears to show humility, but if they are doing it to be seen by others, or thinking that the more they do humble things, the more humble they will become, they fool themselves.

Saint Augustine wrestled long and hard with examining the true motives behind his speech and actions, and what he said in his struggles to be honest about his pridefulness is telling. Here is a sample, extracts, from one section of his 'confessions' (but because he was so verbose, I will just give snippets and hope you can get hold of the full text to read it all).

XXXV "Of such things my life is full, and my one hope is Your immeasurable mercy. For when our heart is made the stage for such things and is over-laden with the throngs of this endless vanity, our prayers are often interrupted and distracted...

XXXVI "You who have curbed my pride with Your fear and tamed my neck to Your yoke. I now bear your yoke and it is light on me, for so You have promised, so you have done; ...tell me whether a third kind of temptation has passed from me or can it ever pass wholly in this life - the desire to be feared and loved by men for no other reason than the joy I get from it, which is no true joy? It is a lamentable state, a base vaingloriousness. From this it comes that men neither love You utterly nor fear You with righteous fear: thus it is that You "resist the proud but give grace to the humble". (The Confessions of Saint Augustine p199-200, F J Sheed, Sheed & Ward, 1978 edition)

That last bit was a quote from what Saint James and Saint Peter both said on the subject, quoting a biblical proverb (Proverb.3:34). James said,

"But God gives us more grace. That is why the Scripture says 'God opposes the proud but gives grace to the humble'." (James 4:6) Peter said:

"Young men, in the same way be submissive to those who are older. All of you, clothe yourselves with humility towards one another because 'God opposes the proud but gives grace to the humble'. Humble yourselves, therefore, under the mighty hand of God, that he may lift you up in due time." (1 Peter 5:5-6)

Jesus also said, "Out of the heart's abundance, the mouth speaks" (Luke 6:45). That is why such a problem as you mention is a problem of the heart. If your heart is full of yourself, your speech will be full of yourself. If your heart is full of Christ, your speech will be full of Christ. How could such a transformation take place? Saint Paul explains:

"Such a person goes into great detail about what he has seen and his unspiritual mind puffs him up with idle notions. He has lost connection with the Head [Christ]... you died with Christ to the basic principles of this world... Such regulations indeed have an appearance of wisdom, with their self-imposed worship, their false humility and their harsh treatment of the body, but they lack any value in restraining sensual indulgence. Since, then, you have been raised with Christ, set your hearts on things above, where Christ is seated at the right hand of God. Set your minds on things above, not on earthly things" (Colossians 2:18-3:17).

I have only quoted snippets from Saint Paul - please get your Bible and study the whole passage. I pray you will find, in it, matters that touch your heart.