Wayne Grudem in his Systematic Theology writes two balanced ideas about prayer:
1. Prayer changes us:
"Prayer is not made so that God can find out what we need, because Jesus tells us, “Your Father knows what you need before you ask him” (Matt. 6:8). God wants us to pray because prayer expresses our trust in God and is a means whereby our trust in him can increase. In fact, perhaps the primary emphasis of the Bible’s teaching on prayer is that we are to pray with faith, which means trust or dependence on God. God as our Creator delights in being trusted by us as his creatures, for an attitude of dependence is most appropriate to the Creator/creature relationship. Praying in humble dependence also indicates that we are genuinely convinced of God’s wisdom, love, goodness, and power—indeed of all of the attributes that make up his excellent character. When we truly pray, we as persons, in the wholeness of our character, are relating to God as a person, in the wholeness of his character. Thus, all that we think or feel about God comes to expression in our prayer.
2. But also Prayer Changes the Way God Acts. James tells us, “You do not have, because you do not ask” (James 4:2). He implies that failure to ask deprives us of what God would otherwise have given to us. We pray, and God responds. Jesus also says, “Ask, and it will be given you; seek, and you will find; knock, and it will be opened to you. For every one who asks receives, and he who seeks finds, and to him who knocks it will be opened” (Luke 11:9–10). He makes a clear connection between seeking things from God and receiving them. When we ask, God responds.
We see this happening many times in the Old Testament. The Lord declared to Moses that he would destroy the people of Israel for their sin (Ex. 32:9–10): “But Moses besought the Lord his God, and said, “O Lord....Turn from your fierce wrath, and repent of this evil against your people”’ (Ex. 32:11–12). Then we read, “And the Lord repented of the evil which he thought to do to his people” (Ex. 32:14). When God threatens to punish his people for their sins he declares, “If my people who are called by my name humble themselves, and pray and seek my face and turn from their wicked ways, then I will hear from heaven, and will forgive their sin and heal their land” (2 Chron. 7:14). If and when God’s people pray (with humility and repentance), then he will hear and forgive them. The prayers of his people clearly affect how God acts."
So for our interaction, how does this knowledge change the way you pray?

How does this knowledge change the way you pray?
It does not change the way I pray, it reinforces my understanding of what Prayer is.
A conversation with God. Thanksgiving for who he is, Giving Thanks for what He has done. Adoration is a good word, not used much anymore.
The knowledge that He is genuinely interested in us as persons, the understanding that He sees the intent of the heart in our prayer, not so much the words used.
Much discussion lately has been on does “God change His Mind? And I’m pleased to see the scriptures posted in this teaching, gives a balanced view,
Not just a balanced view, but based on the full counsel of the Scripture.
This view is contrary to much teaching today where all things are predestinated.
Let’s not confuse God’s foreknowledge, with predestination.
Prayers matters to God, He does listen, He does act, when we pray in accordance with His will. The answers may not always be what we want or expect. But I agree wholeheartedly with the statement here, “The prayers of his people clearly affect how God acts”.
My personal experience with prayers are great, I’m not comfortable so much with public prayers, that is not my gifts, But unselfish intercessional prayers with tears for others, is another gift, and I have seen answers many times that shows me that God hear, and heals,
Those are the prayers that greatly increase my faith. I highly recommend it.
BMS.