I can't answer for USUHS, but Army HPSP works like this:
Usually, during the summer after your 1st year of med school, you will go to Officer Basic Course. The duration has changed since I did it but it's probably about 6 weeks of "fun in the sun" in Texas. I say "usually" because some med schools don't have an extended summer break between 1st and 2nd year, which prevents you from doing it. In these cases you can defer OBC until after you graduate.
After that, you realize, there are no more "summer breaks" from med school. So what you do is an annual "ADT" (Active Duty Training") period with the military. This is a 30-day period where you can go and do a clinical rotation (at ANY time during the year, doesn't have to be summer) at a military medical facility. It is usually in a specialty and at a hospital that you have some interest in for residency -- a chance to see what the program is like and "show your stuff" to the staff. You get to pick where and when you want to go and arrange it with the facility directly. It is unlikely that you would get to go overseas (at least in the Army -- I can't speak for the other branches; however, I did get to go to Tripler in Hawaii for one of mine). During this time you are considered to be on active duty, so you wear the uniform and get paid as a 2nd lieutenent (or an ensign in the navy, I guess). You get 4 of these during your med school career (OBC counts as the first one, so you have 3 others to use as you wish). During your rotation you will get a formal evaluation by whoever your supervisor is and it counts A LOT when you actually apply for military residency.
Hope this helps.