You need a valid OHV registration from your home state to operate an OHV in California. You do not need a Green or Red Sticker or a California Nonresident OHV Use Permit. You will need a California Nonresident OHV Use Permit if your ATV does not have valid registration or a registration program in your home state. This permit allows non-residents to operate by permit for $30 per vehicle. On the website, you can view a Nonresident Permit Vendor List.
Check out these Coachella, CA ATV/OHV resources: