Your cover letter will be the most important part of your resume package. Be sincere about your career change, mention your enrollment at SJC to back up your claims, and avow your commitment to animal care.
Since you haven't yet taken VT courses at SJC, list your resume with Education, Relevant Experience, and Work/Employment History. In "relevant experience" include any and all animal care experience. If you have less than 10 years of work experience, it's best to keep your resume to 1 page. It's not necessary to include "career objective" or "references available upon request" on your resume, but some hiring managers might prefer these.
You may be able to get a kennel/ward attendant, receptionist, veterinary assistant, or other entry-level job in the industry. Check with your vet or your family/friends' vets for opportunities.
Volunteering is a good option for gaining hands-on experience, too. Found Animals Foundation (foundanimals.org)has a Cat Adoption Center in Downey, Adopt & Shop retail adoption center in Lakewood (a new A&S location coming soon to West L.A.), and Spay4LA a mobile service throughout south L.A. The Spay Neuter Project of Los Angeles (snpla.org) offers a volunteer veterinary assistant training program; they have 3 locations: San Pedro, Pico Rivera, and Van Nuys. Humane Society and ASPCA/SPCA-LA are other sources around the southland.
Search volunteer opportunities with animal organizations and see what's near you. Good luck!