Many prayer requests are made known in normal conversation if we would just take notice. Keep a notebook so you can write prayer requests. Don't depend on your memory. If God burdens your heart for someone, assume that praying for that one is always appropriate. Other-mindedness is looking for ways to help and serve others.
Prayer is a tremendously effective way of helping and serving.
Another insight into prayer is to study the prayers of the Bible. Both Colossians and Ephesians contain some wonderful insights into prayer. Many of the Psalms are prayers that give us insight into the nature and character of God. Most study Bibles have some type of indexing to the prayers of the Bible. It is helpful to keep a journal of your Bible study and prayer time.