How does God answer prayers?

After watching this video last night, I've been thinking about how we need to learn how to hear God's answers to our prayers. When I was young, I used to expect some voice to just tell me what to do, or magically all my problems would just be solved without any effort on my part. When that didn't happen, I thought my prayers weren't being answered, but I was wrong. It took decades of painful struggling for me to finally recognize all the personal help the Lord had, and was, giving me.