Be VERY careful with Craigslist. Especially in L.A.
Never EVER go check out a place alone.
Ask for references and actually call them. Seriously, ASK for references of former renters or roommates.
When you do search, have upfront cash, references and all your info ready.
Remember, living in L.A. means basing your entire life - work, friends, hobbies, EVERYTHING - on traffic. Choose your location carefully and listen to locals who know what's up.
Likely the best place to find a living situation will be in the "Valley" i.e., San Fernando Valley. Look in places like Van Nuys, Simi Valley, Granada Hills or Chatsworth. MAYBE Sherman Oaks ($$$$) and MAYBE Encino ($$$$). Remember the Valley is HOT, isolated, and very, very non-diverse. It's a lot of strip malls, chain stores and beige development homes.
If you want to live in L.A. proper, and commute up to Calabasas, live on the West side. Affordable in this area are Mar Vista, Culver City, West Hollywood. And by "affordable" I mean you can score a studio apt. for maybe $1300/mo. That price usually does not include laundry or parking. For that, make it $1500.
Look for rich people in the Valley renting rooms out in their house! That's probably your best bet.