Our actual times when we are on clinics are from May of our second year until January of our junior year, then January until May of our senior year.
The clinical skills course I mentioned is a fairly new addition to the curriculum, and is part of our didactic years. It consists of a once a week lab for your first two years. The goal of it is to bring everyone up to speed on basic skills and client interactions, and they just built a fancy new clinical skills lab which has a ton of cool models. We've done a huge variety of things, including practicing drawing blood on models, placing catheters on models, bandaging large and small animals, learning basics of the computer program they use in the hospital (cornerstone), practice interactions with a fake client (literally we had to talk to a random person in a clinic room and go over an estimate etc, and were critiqued on it), practicing physicals on live dogs including specific labs on orthopedic exams and neuro exams, practicing drug calculations, etc.
During our weekend shifts we are with 2 - 3 other students and a technician, and it's a combination of watching and some hands on stuff - we're given a sheet with things they want us to do, first year it was more basic things like demonstrating placing a catheter on a fake arm, etc, second year we are asked to do more stuff and I was allowed to demonstrate a few things on live animals. We were also taken around and talked through all of the cases currently in that hospital, and if any emergencies came in, we were allowed to watch and stay as long as we wanted (my last large animal shift we had a downed alpaca come in, and I was able to see someone place an over the wire catheter, which I thought was really cool). If you're interested in getting more hands on experience, I'd say clubs are the best way to get it, but you'll get some stuff through the clinical skills course.