Prayer is communication with God. Asking Him for stuff happens in prayer, but if all your prayers are you asking God for stuff, then I'm not surprised that they don't work. Instead, you are supposed to commune with God. Talk to Him. Listen to Him. Tell Him how you honestly feel about what's going on, but don't complain about it. Don't blame Him for the consequences of your actions. It may be best to first understand who you are.
You are a sinner. You're a worthless piece of dung. Your best works are as dirty as menstrual rags to God. There is nothing that you can say or do to get close to God. You don't deserve Him. You deserve to die a horrible and torturous death. Have a nice day. But that's not the end of it. Next, let's look at who God is.
God is a loving Creator. He made man to be with Him forever, but Adam's mistake threw the entire human race away from the presence of our loving God. However, God, being so loving, sent His one and only Son Jesus from Heaven to Earth to live and die as a replacement sacrifice for us. He took that horrible and torturous death upon Himself. We have gotten so used to the cross that we make them out of gold and hang them around our necks as jewelry, but it was an instrument of torture that make the guillotine and the electric chair PG in comparison. God loved us so much that He crawled into our filthy world and let us kill Him. All so that He could suffer the most in order to make His death a worthy sacrifice. This is the God we pray to.
Also, God is the Creator of the universe. He holds it in the span (palm) of His hand. In the way Michael Jordan would palm a basketball, God can do that with the universe. He's a big God. He's a consuming fire, and next to Him, "insignificant" seems too gracious of a word to describe us. What makes us think that we can demand anything of Him?
I've met and talked to people who believe that there is a God, and they believe that God loves them and wants their love in return, so they try and bargain with God, using their "love" as a bargaining chip. "I'll love you," they say, "if you get me..." Of course their terminology is one step closer to the King James Bible, but God sees through that one easily. He isn't impressed by our vocabulary or by any thee's and thou's. He may not even listen to our words but I know He listens to our hearts.
So what's the point of praying to God? Why can't we just feel good things about Him in our hearts?
First of all, God tells us to pray. That should be enough. If it's not enough, then pray anyway. You need it. God wants us to be one inside and out. We cannot be doing bad on the outside and be good on the inside. We can't fool God or take the easy way out. We need to actually pray.
The next thing we need to realize is that Jesus dying on the cross for us washes away our sins. God decides to no longer see sin when He looks at us because every sin we have committed, are committing, or will commit is already paid for on the cross. (That doesn't mean we can go on sinning on purpose. That's an outward sign of a heart that is not following God.) And since God doesn't see sin anymore, we have the freedom to approach God as a child approaches a father.
Prayer is that approach. The power of prayer is the power of the one we pray to. If I fashioned a marshmallow and prayed to it, then the power of that prayer would be only as powerful as the marshmallow. But since I pray to the almighty God, the power of my prayer is limitless. When I approach the Father, I don't just come to Him to dump my problems in His lap. I come to be with Him. My prayer works because I'm with Him. He doesn't have to say, "yes," to all my requests for me to consider my prayer successful. In fact, He tells me, "no," most of the time. So much so that when He does say, "yes," I'm quite surprised. And when I pray, my requests (supplications is the fancy Bible word for requests) are just a small part of my prayer. I spend a lot of time telling Him who He is (not that He needs to know, but if I begin my prayers saying that God is wonderful, more of my requests sound to me like whining) and thanking Him for what He's already done. I realize that I don't even deserve to be alive, and that means that I don't really need to ask Him for anything, since I already have more than I deserve.
But here's the cool part: God loves to bless us anyways. I can still ask for things and He can still give them, but by the time I do ask, I don't even need them anymore. I just think they'd be cool. I just ask in case God is just wanting me to ask. The real thing that I want and the real thing that I need, I already have. An intimate relationship with my Father and Creator. Everything else is just bonus.
Now about answered prayers. God answers prayers. I've seen it happen. He does perform miracles and healings and all sorts of things that we read about in the Bible. He doesn't do it every time we ask, but He does do it when He sees fit. We can't command God like He's a genie. In fact, the more demanding we get, the less likely He's going to do it. When Jesus was teaching and performing miracles left and right, He refused to show the Pharisees a sign when they asked. He's not a performing monkey to do tricks, He's the ruler of the universe and if we can just see a glimpse of who He really is, our prayers would change dramatically.
So to see God, I can only recommend reading the Bible (yes, the whole thing) and praying. God will reveal Himself through His word and through prayer. Just seek Him.
Some Bible verses that I've been contemplating while writing this are Matthew 6:8-13, 12:38-42, 18:19-20, and James 4:2-7. Be sure to read those verses in context, so you know what God is really talking about. Pray about them before during and after your reading and I'm certain God will reveal Himself to you. It is, after all, what He wants to do anyways.