The most important thing is visibility. Be where the motorists, and the pedestrians, and the other cyclists, expect you to be. Don't weave. Don't stop suddenly, or change lanes without signaling. Don't ride on the wrong side of the street, or on sidewalks.
The other main piece of advice? Cars are super dangerous, but unless you're a complete dumbass, most of your accidents will be from unexpected objects in your path. Watch out for potholes, sticks, or slippery conditions.