Prayer is not primarily/just a means of asking God for stuff. In Matthew 6:9-13 Jesus does a brilliant job of correcting our ideas on prayer when he teaches the disciples (and us!) "The Lord's Prayer". Jesus after all is the perfect teacher here. He is God and Man and knows what pleases his Father but knows our human situation too.
The focus of the prayer is on God and not us - especially in the first half. Then the second half we express our relationship with God.
Starting with "Our Father in Heaven" we're expressing that God is our Father (thanks to Jesus!) but that he is also heavenly (i.e. holy, holy, holy).
We pray that His name (character) is hallowed (honoured as holy) and we express a desire to see His kingdom come.
It teaches us to pray things like "Your will be done" rather than "God, please do my will".
We pray that God will provide what we need and that we are constantly reminded of our dependence on him when we say "Give us today our daily bread". And so on.
I can recommend this book on the Lord's Prayer which I read recently: Our Father (Enjoying God in Prayer) by Richard Coekin
In terms of rationalising prayers in the light of predestination, I think Luke 11:11-13 is helpful. It compares God to a good earthly Father who when asked by his children will not given them bad things. I think the parental comparison is good. Parents know that their children need things (i.e. they buy food in advance) and will give thing to them but it's so much better when a child humbly asks and thanks their parents.