The first thing that you need to know is that, unlike skateboards, roller skates, kick scooters, and any other sort of human-powered wheeled conveyance, bicycles are considered vehicles under California law. That means that, for the most part, you have all the rights-- and all the responsibilities-- of motor vehicles in the public right of way. That means that, yes, all of those pesky car laws apply to you too, cyclist. Ride on the right-hand side of the road, with traffic. Stop at all red lights and stop signs, signal your turns, and obey the speed limit (although that's usually an easy one on a bike). For turn signals, hold out your arm straight and level in the direction of your intended turn. (CVC 21200(a))
On the flip side, bicycles are permitted on nearly all public roadways in the state. They're banned from most freeways (but not all), but that's it. As a cyclist, you're entitled to use the right-most lane that travels in your intended direction. That means that you're allowed to use left-hand turn lanes, and you do not need to stay in a right-hand turn lane unless you're turning right. Ordinarily, you're required to stay as far to the right as
- when turning left.
- when passing another vehicle traveling in the same direction.
- when approaching a place where a right turn is permitted.
- when necessary to avoid road conditions such as debris, surface hazards, other bicycles, pedestrians, parked cars, etc. or when the lane is "of substandard width"-- that is, when the lane is too narrow for a "vehicle" to safely pass a cyclist. I generally interpret this section by replacing the word "vehicle" with the words "full-size bus," and the words "safely pass" with the words "pass with 3 feet of clearance."
- You may also ride on the left-hand side of a one-way street.
If a bicycle lane or path is provided along your travel route, you are generally required to use it. That said, you are allowed to leave the lane should travel conditions within it become unsafe, or in order to pass another vehicle or avoid a hazard. (CVC 21208)
Your bicycle must be equipped with a brake that will cause one braked wheel to skid on dry, level, clean pavement. Fixie riders, this means that going brakeless is illegal, although you'll probably get a fix-it ticket if caught. Invest in a front brake. You must also be able to put your foot down, as well as hold on to the handlebars without raising your arms above your head. On most bikes, this isn't a problem. (CVC 21201)
If you're riding at night, you are required to have a white headlight and reflectors on your pedals (or shoes or ankles- these are good if you're riding clipless), sides, and rear. Everything should be either white or yellow except the rear reflector, which should be red. Your bicycle should come with all of these reflectors already installed. You may use a red light in lieu of the red rear reflector, and a headlamp attached to you in lieu of one attached to your bicycle. So you should already have the reflectors-- an inexpensive LED light set can have you legal for night riding in no time. (Of course, tiny LED lights won't make night riding safe. If you plan on riding at night a lot, you should look into getting a much brighter headlight.) (CVC 21201)
All of the above are state regulations, but there are also a few local laws to be aware of. RMC 10.64.170 requires that you park your bicycle in a bike rack while downtown-- a feat made much easier with addition of a couple dozen new bike racks downtown, which I'll post about in a bit. It only applies if a rack is available within 150 feet. 10.64.310 prohibits riding on the sidewalk unless there are signs specifically permitting cyclists. (The only such signs in the City that I'm aware of are at University/Iowa, in Arlington Village where the bike lane joins the sidewalk, and along the Victoria Ave. path.) There are also a good number of provisions that simply restate requirements in the CVC, albeit often less elegantly. (RMC 10.64.330, for example, is the equivalent to 21201, but it doesn't make the exceptions to riding to the right clear.)
Sorry that was long, but this is a reasonable summary of the rules and regulations that apply to you while you're riding your bicycle. I'm not going to say that you should always obey every law, but by knowing them you can make an informed choice about them.