What are the classes to take to become a veterinarian at UCLA?

You cannot become a veterinarian at UCLA; the two veterinary schools in California are UC-Davis and Western University. However, you can take the courses needed to apply to vet school at UCLA - you will need to take lots of Biology (zoology, microbiology, anatomy, genetics, etc.) and chemistry (inorganic chemistry, organic chemistry, biochemistry) as well as physics, calculus, and multiple general education classes.

The list of pre-requisite classes can be found at UC-Davis' website.