Most of my prayer might more properly be considered meditation, in that it has an inward focus. I do not agree with Oberon's distinction that seems to equate meditation with absence of a supreme being. I do believe in deity, though not in any traditional Judaeo-Christian sense, and deity is often a subject of my meditation.
When I do pray specifically "for something", it is almost always for the strength and knowledge to do what needs to be done, for openness to opportunity that may present itself, for clarity to see my own failings. I do not expect "God" to do things for me. I expect instead to be empowered or guided to do them for myself, or to make the right connections, relationships, etc. to get the human help I need. I pray in a similar fashion when I pray for others in need. That is, I ask the divine to give them the strength and resources to cope with their difficulties, to work through them and to learn/benefit in whatever way possible, rather than simply to have them magically vanish.
I find prayer/meditation works, but mostly for me. Meaning, I feel I can influence my own outcomes much more readily than the outcomes for others. This relates to the idea, expressed by others, that prayer and meditation mostly change ourselves, in ways that might happen even if there is no god at all. I feel that prayer and meditation help me focus better, see things I may have overlooked, align my goals with my values, gain new realizations, and generally marshal my own resources to more effective use.
There are some set words/prayers I use repeatedly, but generally it is more free-form, and it does not always involves words.