You don't get "lined up" with the other classes unless it works out just perfectly. You finish 7th semester and generally have anywhere from a week to a month to get yourself moved to your clinical school before you start clinics, regardless of what time of year you finish 7th semester. While I was in clinics, there were 2 times during the year where we randomly got more island students because of the differences in scheduling between island and US schools. You do you clinical year for the equivalent of a year. So if you start clinics in January, you typically will finish around the following January. The process is such a well-oiled machine at this point. If you start at Ross in the September class, you'd start clinics after the Christmas Break, most likely the first or second week in January. You'd finish clinics the following January.
As far as what you're doing while you're in clinics-- you're rotating in and out of different areas within the hospital. Unless you're on externship or off-campus rotations, you'll be in either the small or large animal teaching hospitals. Rotations are usually 2-3 weeks long. For instance you'd be on maybe internal medicine rotation where that's all you do- you take in and work up internal medicine cases while caring for any inpatients that are on your service. Then you'd rotate to something like surgery or a large animal rotation.
Does that all make sense?