Sometimes we pray and God lays on us the thing we really wanted or needed, or lifts away the thing we wanted to get rid of. This is what we usually mean when we say "God answered my prayer."
But God doesn't always do this. Sometimes I pray and the circumstances don't change but I find myself calmer, at peace with the situation. This too is an answer to prayer.
And sometimes too, I pray, the circumstances I prayed about don't change, and how I feel about those circumstances doesn't change either. This is when prayer feels most unanswered. But maybe the answer is "trust and wait."
But let me not base my strategy of prayer, or my desire to pray, on thinking one and only one of these three things is the norm. Paul Miller presented this issue in the first chapter of A Praying Life. He's camping with his daughter, and she tells him she's lost her contact lens. He looks at the ground covered with leaves and twigs and says "lets pray." His daughter says "what good will that do," in despair because her prayers for her autistic sister to speak had not been answered. Paul prayed silently "Lord, this would be a good time to come through," then prayed aloud to find the lost lens, and then they saw it, sitting on top of a leaf.
Paul and his daughter saw God respond by revealing the missing contact, showing them he could and would answer some prayers with a quick fix, even though in the situation with the autistic daughter, he was not doing so.