When people say that God never answers their prayers, what they are really saying is they prayed and didn't like the answer. No is as much of an answer as yes. So if you have prayed for something and God said no, don't say that God didn't answer your prayers. It is more accurate to say that you didn't like the answer God gave you.
The primary objective of prayer is to align your will with God's will. As 1 John 5:14 tells us, "Now this is the confidence that we have in Him, that if we ask anything according to His will, He hears us." So if you want to see your prayers answered in the affirmative, if you want God to say yes to your prayers more often, then you must pray according to the will of God.
Jesus taught His disciples to pray, "Your kingdom come. Your will be done on earth as it is in Heaven" (Luke 11:2). True praying is not overcoming God's reluctance; it is laying hold of His willingness. Prayer is not getting your will in Heaven; it is getting God's will on earth.
When you have lived for awhile, you begin to understand that God knows more than you do. And you even will thank God for unanswered prayers. You will thank God that He said no to you at an earlier time, because you will realize, with 20/20 hindsight, that you didn't know what you were asking for at the time. So don't ever be afraid to pray, "Your kingdom come. Your will be done on earth as it is in Heaven" (Luke 11:2).
The goal is to pray according to God's will. And nothing lies outside the reach of prayer except that which lies outside of the will of God.