I definitely agree with Emily. Some vets might not like you 'interfering' too much, and I have been at a vet practice like this, and you don't learn much at all.
But the most common experience is that the vets/nurses will really appreciate the extra help, and as long as you're polite and punctual, they should be happy to answer your questions.
I used to take a notebook and make case notes, then go home and google the drugs used, learn a bit more about the condition, and this is really useful with in-patients and follow ups - you'll feel much more involved!
Learning how everyone prefers their tea/coffee = WIN, helping to weigh the animal, cleaning the examining table, or if the vet is taking blood, have everything he/she needs laid out for him/her, etc. Help with restraining animals.
But the first day I would just kind of observe the way the vet surgery works, and see what they would deem appropriate/inappropriate. You probably have to 'prove' yourself, and they'lll start trusting you more and more over time.