Interesting. I'm actually looking to go to the UMUHS (Uniformed Medical University of Health Services, hooray for abbreviations)... Luckily, my school hasn't kicked military recruiters out (at least not to my knowledge) so I can learn a bit from them. But Westpoint would be fun, albeit very close to home.
Do you do horseback riding or shooting sports or fencing? Those are all big plusses for getting into West Point (or so the grapevine says :-). I think they're looking for Modern Pentathlon competitors!
You can get all the application information from the academies' web sites. I think some of them will even provide a contact in your area who's been through the process and can advise you. (You could probably find this on FR, too.)