A "sub-i" is a sub-internship, a rotation where a medical student, typically a 4th year, is treated as much like an intern as possible. Where I'm at we really don't use that term much partially because we do two medicine rotations and the second one is treated like a sub-i. I don't think it matters much if the rotation is called a sub-i or not; either way, you'll want to take on as much responsibility and your skills and supervising residents and attendings allow. Rotations where you're a primary service (as opposed to a consult service) are better as you get more responsibility. I've been told that busier services are better, although I got to imagine thats only true to a point. If you have a particular reason to try to rotate with somebody famous or who does research in an area you're active in, you can always try to contact him/her and coordinate. Away rotations are also golden for getting letters of recommendation, as it seems most prestigious places like to have a LOR from someone they know and trust, and there's probably no better way to prove that you get along well with the culture of the program than to spend a busy month on service at a program and do well. Rotating at a program is also a good way to show that you're serious about going there. Not only is it a time for you to show off, but it's also a time for you to get a very candid look at the program. Because of the relationship between aways and residency, I think most people try to do away rotations around the summer before their 4th year or very early in their 4th year (June, July, August, September). Some programs will let you interview during your away rotation, especially if you're from far away.
I really don't think that away rotations are necessary at all as long as your coming from a respected program and have good LORs. I suppose multiple away rotations might help you really get a feel for where you want to do residency and may increase your chances of getting a prestigious LOR.
I found that each place I was interested in rotating at had info either on the webpage of the medical school, their IM program, or dept. of medicine webpage. I just Googled the university I was interested in to find the appropriate webpage (try "University of X visiting medical student"). If that didn't work I poked around their main medical school webpage. If that fails I suppose you can call or email. It's not easy. Here are a few links I had saved in my search; my apologies for dead links:
http://www.mayo.edu/mms/clerk-eligibility.html
http://pritzker.bsd.uchicago.edu/students/index.html?content=visiting.html
http://www.medschool.northwestern.edu/education/visiting_students/
http://www.med.umich.edu/medschool/visiting/
http://www.uwmedicine.org/Education/MDProgram/StudentAffairsAndServices/Registration/vsprogram.htm
http://aladdin.wustl.edu/medstudents/eletvcat.nsf/
From what I saw, the deadlines varied. The schools I looked at had various deadlines, but were generally in March, April, and May for fourth year rotations beginning around July or August.
I pretty quickly focused in on a rotation at Mayo - Rochester. Mayo's application is pretty difficult - they require a personal statement, one LOR for US students and two for foreign students, a transcript, CV, and an outline of your research. The good part is that once you have done the Mayo away application your residency application is almost done. Their deadlines are rolling last I saw (for rotations Jan-March by Oct 1, April-June by Jan 1, July-Sept by April 1, Oct-Dec by July 1). You submit your top 4 choices of dates and rotations. The rotations are all 4 weeks long and can start any week.
