The National Student Research Forum is a very accessible way to get your feet wet in presenting med student research and winning a research award prize. I did it last year and it was a wonderful experience. They give several awards in different research categories and money ($200 each prize).
The ACP medical student research competition is also another way of winning a prize. They pick 10 winners in basic science and clinical vignette categories and give all expense paid trips out to the ACP national conference to present either poster presentations or oral presentations. I did this past year when it was in SF and it was pretty fun.