The first rule to remember is no one has true "right" of way. Anyone is obligated to yield if another car is within the intersection or so close as to present a hazard. Also, you'll want to yield to pedestrians. That said, there are some rules to remember for each type of intersection:
Left turners yield to drivers who are turning right or going straight.
Generally, this rule applies: First to arrive, first to drive. If drivers arrive at the same time, the driver to the right goes first. If two cars arrive at the same time and are facing each other, the driver going straight goes first. If you're turning right, and the car across from you is going straight, it's OK to turn right at the same time.
You'll stay safe when you follow the rule, "Top of the T goes before me."