With me, prayer is more like an aside. I'll be thinking about something, really chewing on it or wrestling with it, not thinking of God at all, but then at some point a part of my brain will say, "What do You think, God?" And then I’ll get the answer.
(And, if you don’t mind my saying so, sometimes the answer is a little flip, but I've come to expect that from God because He usually doesn't waste time beating around the bush or sugar-coating it for me. ... But I digress.)
Jesus tells us that God already knows what we need, so praying for what we want is an exercise in redundancy. And Jesus also promised that God will provide what we need.
The great Christian theologian and Phillies center-fielder, Gary Matthews, once said that he believed that all prayers are answered, but that sometimes we don't like the answers.
So we need to distinguish between what we want and what we need.
I once heard a sermon about prayer that drew on the story of the death of King David's first-born son by Bathsheba. (2 Sam. 12:1-23) David had arranged for Bathsheba's husband, Uriah, to die in battle, and then David took Bathsheba as his wife. This "displeased the Lord," and God told David that Bathsheba's son by David would die. According to the Bible, David pleaded with God, fasted, and prostrated himself on the ground for six days. On the seventh day, the child died, and then David got up, washed, went to the temple to worship God, and then ate. His servants couldn't understand why David would fast and weep while the child was alive, but get up and eat once the child was dead. David explained, "While the child was still alive, I fasted and wept; for I said 'Who knows? The Lord may be gracious to me, and the child may live.' But now he is dead; why should I fast? Can I bring him back again? I shall go to him, but he will not return to me." (2 Sam. 12:22-23)
The preacher used this as an example of the failure of prayer, but it is actually an example of success. David got what he needed, even though he didn't get what he wanted. What David needed was humility and the strength to accept God's will (i.e., the death of his son), and David got those things from his prayers. So David's prayers were answered, even though David didn't like the answer.
I sometimes think of prayer as a "reset" button for our brains. When a computer gets so hopelessly confused and messed up that it doesn't operate properly any more, the solution is to "reset" the system and start all over, with a clear memory and all of the operating priorities back in order. Similarly, prayer is I how lose the crazy thoughts with which I have become obsessed and am able to reconnect with God.
Which is what I usually need.