SoCal describes well the legalities and options of flying here in the US and California.
As for the practical flying, yes, the LA basin can be overwhelming when it comes to ATC and airspace - it's easy to bust B and C airspace as it's all packed quite tightly together. It made me quiver just thinking about talking on the radio when I started here, but one learns. That said, there are also some tremendous freedoms here (like crossing LAX at 2500ft) or landing at Hawthorne where you're side by side with big 747's on final to LAX. There's also a surprising amount of G and E airspace around, so if you want to minimize talking on the radio, there's ample space for that.
ATC like to speak fast and they often assume you're familiar with their airspace. If you're not, make sure you say "unfamiliar" or otherwise make clear that you're a visitor and they'll help you out. ATC is very professional and helpful here, as in most places, as long as you're not afraid to ask for help. Americans love abbreviations and shortenings, so they'll throw you a few of those quite regularly. If you don't know what they're talking about, call them on it - they'll explain. "Cleared via LMU for mini route, squawk 2077". This is a common instruction for the LAX crossing from Santa Monica Airport. LMU, is Loyola Marymount University. It would be just as quick to say Loyola, but as I said, they love abbreviations. And it's not marked on the main chart either, it's on the infold on the Terminal Aera Chart.
Please familiarize yourself with US charts, and specifically the LA Sectional and Termina charts. It looks overwhelming at first, but it's actually not that bad.
SkyVector: Flight Planning / Aeronautical Charts
Sticklers, and I mean sticklers, for correct ATC and familiarity with procedures is Long Beach Airport. If you're easily spooked, stay away from that airfield.
Santa Monica Airport is probably the most lax, as long as you understand that Rwy 21 (which is used 99% of the time) has both right and left circuits operating simultaneously and you can often lose track of who's number three or whatever. On top of this biz jets on IFR plans get straight ins. If it's really busy, the tower will call your base but you can also request them to do so in case you can't keep track of everyone inbound.
Whiteman has a very grumpy tower guy, but is otherwise a nice field.
Van Nuys is very busy, but a good airfield. You'll mix with a lot of biz jets, so you need to be on point.
Camarillo is also busy, but in a more relaxed pleasure flight way. They have a great restaurant overlooking the apron.
Burbank is big jets, but you can get in there. I haven't tried myself. That's what's nice here, small aircraft are not excluded and shunned like pariahs like in Europe. They all co-exist nicely with the bigger boys at the same airports.