This is simple, but it does require one to wear their "big boy pants". Decide where you want to rotate, then call that school's deans office. You will be handed off to someone who will tell you want is required (generally documentation that you ARE a med student from the institution you claim, that you have been given malpractice insurance through your school and that it will extend to theirs, and that you are all nicely immunized and not exposed to TB), next you will need to obtain departmental approval, ie. If you want to do IM at said place, the IM people will have to give their ok. Next find out who the point of contact is for students in that department, generally a secretary, who (and be nice to the secretaries kids, these people can sink your boat almost faster than showing up to rounds drunk and grabbing a nurses boob) will tell you which attending to speak to. Email said attending about your interest and that he should be expecting papers from the SOM (you KNOW he's very busy but you would very much appreciate his attention at his earliest convenience) - also call (you wont get them, but leave a polite message).
Then when you have all the paperwork back, take it to your school to get final approval. One of the secretaries in the deans office will be able to walk you through your school's specific requirements.
Its kind of a pain really - and you have to stay on top of it everyday until final approval comes down form on-high.