First, you'll need a BS degree. You can probably choose any field of science, but some branch of biology would be best. Getting your BS degree at a UC, even if you start your first couple of years at a community college (smaller classes and you'll save a LOT of money!), will probably take 4-5 years. You'll want to get an internship at a vet office during college. After that, you'll go to vet school. UC Davis has a great vet school click
Their website can probably tell you how many years it typically takes to become a doctor of veterinary medicine.