Pedestrians who have stepped off the curb onto a crosswalk have the legal right of way.
In practice, some people stop, but many people don't. But at any rate, people behind you will not think you're completely idiotic if you do stop.
When the light is red, you can make a right turn after stopping. There are also lots of (unmarked) ``yield'' turn lanes in which you need not stop before proceeding, but any accident you get into is automatically your fault. You can make a left turn directly into any lane on a green light, but look out for cars making turns with you in the next lane! For right turns, you should stick to the right-most lane. U-turns are legal in most places, provided traffic is clear.
Four-way stops are popular in California, especially on the Stanford campus. The law is that if you get there first, you can go first. If two cars arrive at the intersection at the same time, the one to the right has the right of way. In practice everyone waves at each other. Many people don't really stop. Officially, cyclists must stop (they must obey all road signs), but the unofficial rule is that bicycles don't stop. However, the police crack down on this every now and then, so take care (as either a motorist or a cyclist). Look for bicycles behind you when turning right.