There is a lot of information on "dream recall"'dream recall' related to research on lucid dreaming. For some quick information, I would take a look at this page:
I have tried some of these techniques, and I found that what has worked for me in the past was
- trying to write down everything I can as soon as I wake up
- lying in bed, not moving, and just letting my mind wander over what I could remember (this usually helps other memories about the dream pop up)
- doing this consistently every day.
The last one is the most important, you really notice that if you are consistent you start remembering more and more when you wake up. I highly recommend the book "Exploring the World of Lucid Dreaming" by "Exploring the World of Lucid Dreaming" by Howard Rheingold and Stephen LaBerge. It was the required reading for a Psychology of Dreams class I took and is based on a lot of cool research.