Here's what John Calvin says about Psalm 119:13. This selection is also very insightful and helpful.
Verse 13: With my lips I declare all the rules of your mouth.
David shows here the accord which ought to be betwixt God and us: to wit, that God has instructed us, and when we have heard that which has been said to us, that everyone should say “Amen,” and that there be a sweet harmony and accord betwixt him and us, without jar or contradiction.
Behold here the summary of what is meant in this verse. Note that David declares that he contents not himself alone with following of God and cleaving to him: but that he labors and desires as much as lies in him, to stir up his neighbors likewise, and to bring it so to pass, as that God might be served with a common accord, throughout the whole world. He then that will have a true zeal to honor everywhere, and seek by all means possible that he can, to redress those which are wickedly given, to stir up those which are cold and negligent, to strengthen those which are weak and feeble, to entertain those which are already in a good earnestness, and to make them more earnest.––And indeed, these are the very things which all the faithful seek to do.––For the Lord our God teaches us upon this condition, that every one of us think not only particularly of himself, but that we should also have a mutual care one of another, and whensoever we shall have this zeal, let us understand, that God has created the whole world upon this condition, that we all should be obedient to him.
But we must well notice the order that is here set down: For David does not begin with this sentence, “That with his lips he has told of all the Judgments of the Lord’s mouth.” For he has said before, that he "has hid them in his heart." The thing which David said to be hid in his heart, he soon after declares it with his mouth, wherein he shows that every one of us ought to begin with himself. When we mean to instruct and teach our neighbors, we must not say to them, “Go you before:” but, “Come next after me, or else hard by me:” and having care all to go the right way, we should all at once labor to go together to our God, to be conjoined to him in true faith. And I speak it to this end, because we shall see many who in this behalf can very well prattle and babble, and would seem to be the greatest doctors in the world. But what of all this? Let us in the meantime look into their lives and conversation, and we shall find in them nothing but infection and stench, nothing else but mocking of God in all they go about and do. We must therefore follow the order which David here holds: to wit, that the word of God be his as a Treasure in the bottom of our heart: and afterward when as we shall have this affection, let us endeavor ourselves to draw others also thereto, and go altogether with one accord to honor our Lord God; and that he which hath been better taught than any of his neighbors have been, let him confess that he is so much the more beholden and bound unto God, to do that which is here showed unto us by David.
For although we are not all Prophets as he was, yet for all that, this was spoken to us all in general, “Admonish ye one another.” Saint Paul (1 Thess. 5:14, Col. 3:16, and Heb. 3:13) speaks it to all the faithful and to all Christians. And that we should also know that this belongs and pertains to us: and chiefly as I have before said, that they which are most earnest, should lay forth the grace which was given unto them for the common building up of the Church, and instruction of their neighbors.