(It may be possible to pray without believing in a personal God, but I don't personally know how to do that.)
Prayer is sometimes expressed in one of five ways, called:
1.Praise: Praising God (for me) is above all a way of getting my mind off myself, that irresistably fascinating subject. A great many of the Psalms are Songs of Praise, likewise Church Hymns. Entering into them is very healing. (For years the hymns meant primarily the music to me; I can whistle a raft of hymns, but ask for the words: I'm too often blank. Now, in the autumn of life, I'm trying to focus on the words (as Ellie does), and I find it tremendously rewarding.)
2. Thanksgiving: Above all give thanks; express gratitude. If you want God's ear, there is no better way. An asthmatic, I thank God for my breath; when the breath God give us stops, we die (physically, that is). We Americans have no idea how fortunate we are in material blessings, which leads to a lack of gratitude. People resent not being thanked for things they do. How about God?
3. Confession: it's good for the soul, we've all heard. It's the best way to get real. Give up our illusions about how good we are, how generous, how long suffering. That leads to all sorts of neuroticism, but confessing who you really are leads to healing humility and peace within yourself.
4. Intercession: To pray for others is a great thing to do. (Once, newly converted to the love of God, it spread out so that I found a young man, same name as me, but much younger, who was terribly needy-- psychologically. I wanted so badly to help Larry that I prayed (maybe my first honest prayer); Lord, help me to help him. I wanted to so badly that in desperation I prayed a Jacob-like prayer, Lord, if you'll let me help Larry I'll do anything for you. With a sob: I'll even be a minister.
Well you know what? I realized that's what I wanted, and from that day 49 years ago I've never thought of myself as, or wanted to be other than a minister. PTL.)
5. Petition: here's the one most of those in what David calls Popular Religion resort to. God, gimme this, gimme that, whatever. Lord save my poor sick child or whoever. God may not do it, then what. Do you resent him from then on? Unfortunately some poor people do.
There's one glorious petition you can't go wrong with: Purity of Heart is to Will One Thing Do you know what that thing is?
Here is an addition that I should have included:
The Jesus Prayer: something like this: inspire: Jesus Christ, Son of God; expire: Have mercy on me a sinner. Synchonize those thoughts with your respiration. This is widely used by Eastern Orthodox Christians. Although I haven't made a practice to praying to Jesus, I have recently seen real value in this special prayer. It's actually a more of contemplation. In times of stress I resort to the Jesus Prayer; I become quieter, see things in proportion, and find the the (self-induced) stress is not at all necessary. Try it if you feel led in that direction.