Greetings JH,
I can understand what you are feeling when you post this. If I may share this, perhaps this could be of some help to you. You initially ask:
"What does God expect us to ask for in prayer?"
The truth is, contrary to what others have said, God wants us to be honest. He doesn't 'expect' anything from us, but he does desire us to be as honest as we can when we do pray to him. You see, when one comes to the Father by means of his Son, the Father and the Son already knows what it is you want and even why it is you are coming to them. They know what you are expecting and they know why it is you ask for what you are asking for. So, since they already know all of this, and nothing is ever hidden from their eyes.. it is for your own good that when you do come to them, you are honest about what it is you really want to say.
You mentioned you feel that nothing happens when you pray. This could be because of a number of reasons. First, God does not get offended by the things you ask of him. In a case like this he does not get offended even when you are dishonest about what it is you really want. When you come to him and are dishonest about what it is you really want.. you are really only hurting yourself because you don't ask for what it is you really want and because you were dishonest about what you really want, whatever it is that you did ask for will not satisfy you because that is not what you really want. In fact, it is very possible that the thing you asked for could be more troublesome for you than it is worth. So it is best to be honest.
JH, you can ask for money, health, material things, the truth about the Bible, and wisdom; but what you must understand is.. why is it you are asking for these things? For example, if you ask for money, why is it you are asking for money? Are you asking for money because you want to pay bills, be rich, have peace of mind? If it is to pay bills, why is it that you want so much to pay bills? These bills that you have, why did you put yourself in a situation where you would need to pay these bills? It is important to ask this because if you are in a position where you are unable to pay these bills, did you honestly learn your lesson in misjudgment so that you do not put yourself in that position again? What have you done to have better judgment? These are questions you want to ask yourself because.. IF one is praying for money to pay their bills.. many times they do not realize that what they are really asking for is to have better judgment when making decisions, and that the paying of the bills was just one of the reasons why they desire better judgment.
Concerning wisdom, the Father is ALWAYS at all times HAPPY to give wisdom to anyone asking... always. If you have asked for wisdom, it is very possible that wisdom for some time has been "coming to you" but you have been 'casting it away' from you not realizing what you were doing. Something that has always been true for all people is this, "If you want something, you must give something up." To have wisdom involves having better judgment. One of the things that cause bad judgment is our desires. When something is offered to us and it "stimulates" us.. many times we jump for it and later REGRET it. This happens when people buy a car or a house and later realize that it is "not exactly" what they were looking for. Perhaps they wanted something less expensive or more detailed. Possessing wisdom requires one to give up their desire to do what they want to do or "like to do" and do what is best. For example, if one were a child and he decided he wanted to be wise, he would have to give up many traits of being a child. This includes getting angry when they don't get what they want, learning to have good priorities even when it seems to impede on their freedom, when something exciting comes along instead of jumping at the first thing that excites them they must learn to discern and be careful with their choices. It is the same for adults. If an adult wishes to have wisdom, they must learn to "deny their flesh" and start looking at things for what they are and not for what they want them to be. They must do this if they want to be wise with money, housing, business, employment, relationships, etc. They must learn patience, understanding, honesty, and care. These things.. and others.. are necessary in order to have good judgment. YET.. one cannto have any of these things unless they look inside themselves and see in their own selves what desires and traits and reasons for these traits they have in themselves that are causing them not to have patience, understanding, honesty, etc. One must admit they don't have it first.. before they can see why. Once they see they are lacking.. they must search out in themselves honestly why they are "the way they are." When one understands why they are "the way they are".. it is then that they can change and become something better.. by denying and giving up the things IN them that made them the way they were.
If you are honest with yourself, this process will be easier for you. If you are the type of person that likes to hide and think you are a 'good' person competent in many things.. it will be HARDER for you to see yourself for who you really are and even HARDER to improve yourself to become something better.
These things will help you get an understanding about yourself and then when you come to God in prayer, it will be easier for you to 'hear' his responses to you as to the things that are 'best' for you.