It's really pretty variable. You can do whatever you want to do.
Some people go home and work in clinics. Some people work on fishing boats in Alaska. Some people do research. Others work at Starbucks. The lucky few go backpacking in Europe.
The teaching hospital may offer jobs or unpaid learning opportunities (experience in large animal, small animal, etc). Generally the school will not offer any classes for vet students.
I've know people who have: gone off to research whales, worked for Banfield, worked in clinics, traveled, or just did nothing.