I actually started volunteering at a vet clinic when I was 6. My hamster wasn't well and a new vet clinic opened up down the street with a brand-spanking new veterinarian fresh out of school.

My hammy died, but I was absolutely hooked. I've been wanting to be a vet ever since. He let me "assist" during surgery (adjusting the light, giving him some instruments), and just hang out with him after school and "help" him with the animals. He eventually turned his clinic into a major hospital and I'm thinking he's probably retired now (this was another time and another place on another continent).

But I digress... you can probably volunteer at any vet clinic you feel some comraderie with.