I'm not from the LA area so unfortunately I can't offer specific local resources. My advice for your first 1-10 births would be to find clients looking for a low-cost option and maybe charge $100-$300. Of course you could also volunteer your services for no cost, but I think it's okay to charge a minimal fee to cover the expenses you're paying (gas, parking, the bare minimum supplies you'll carry in your doula bag, etc). Perhaps you could make some posts on neighborhood list-servs, on-line mom communities/list-servs, etc advertising your low-cost doula services as you start out.You could also make a flyer and post it at various places around your neighborhood (grocery stores, baby boutique type places, etc.) I'd imagine that you'd get more than enough interest in your services (going off of the market where I'm living anyway).
If you wanted to volunteer, you could email various women's health clinics, midwifery practices, birth centers, your local WIC office, etc. Usually they are more than willing to refer doulas who are offering low/no cost doula services because they know clients who could benefit from having the extra support.
I hope that helps! Just don't be afraid to put your name out there and go for it!
Do you have a website up already?