How does a Mexican trained veterinarian get accredited here in the USA?

You will need to pass the Educational Commision for Foreign Veterinary Graduates (ECFVG), which is a test of your veterinary knowledge covering everything from diagnostic test to surgical techniques. Once you have this, you can apply for a license from the State licensing board where you want to work at, which generally involves another test that is specific to that state.

With those two items you can work as a veterinarian in the United States. However, most veterinarians also need a DEA license (to legally handle controlled substances like opioids) and federal accreditation (to legally sign rabies certificates and health certificates).