I think that one good way to let our prayers come out, is to let them flow out of us in the form of poetry. We can let the emotions and the rhythm of our thoughts take shape, take tangible shape, this way. I'm not a very good poet myself, but when I pray, I feel that I could be. We can also use writing to channel and discipline our prayers. Many people find that writing a journal helps them to say the things which seem too difficult, or too fearful, to share in any other way.
Spiritual journals are definitely a form of prayer.
Prayer can also take the form of action . Washing each others' feet is one way mentioned in the gospel. Service to our neighbor. Caring for people. I know people who pray while they're ironing.