L.A.'s no better or worse than anywhere else, and all the rules and pitfalls apply.
Rule #1: Among musicians, the nice guys finish first. If there are a dozen amazing players who are overly aggressive or cocky, and one guy who's pretty good and makes everyone comfortable, guess who gets the gig?
#2: Network and get known. Every little thing (like frequenting jam sessions) can pay off.
#3: Unless the pay is ridiculous or nonexistent, or unless you're already booked, never turn down a gig, or you'll soon be known as the guy who turns down gigs and the calls will stop. Be the guy who gladly takes gigs, and you'll get called and recommended more often. Some nights will pay $75, some $125, some $50. Do 'em all. Don't be one of those guys who won't walk out the door for less than $100, or you'll find yourself sitting at home a lot.
#4: Seek auditions and promote yourself online as an L.A. player, and be a nice guy about it (did I already mention that?)
#5: For auditions and gigs, keep it simple. Bring a 4-pc kit, play 2&4, and you'll work a lot. In L.A., you get paid to play oldies, classic rock, & blues. If you're under 40, start boning up on your Beatles, Stones, Kinks, Cream, Animals, Creedence, Hendrix, Led Zep, Motown, and every one-hit wonder from the '60s. The paying jazz/fusion/funk gigs are few and far between. Don't turn 'em down, but don't expect to make much money. Consider them good networking opportunities.
#6: No shame in having a day gig... I assume you like to eat and have a roof over your head?
Besides, most of the guys you'll be playing with will also have day jobs, so your schedules and availability will be similar.
Good luck and welcome!
Bermuda