There are two basic things that can go wrong with a swimming pool light. Either the bulb burns out or it gets water in it. Leaks in swimming pool lights used to be a major danger. But now that sensitive circuit breakers are compulsory for pool lights, they usually just make the light turn off and require the replacement of one or two parts. If the problem is a burnt out lightbulb, all you have to do is change it.
Press the reset button on the ground fault circuit interrupter. If this turns on your pool light, then it was simply tripped accidentally. If your pool light stays off, you most likely have a burned out light. If the GFCI immediately trips, you have a short in the light.
Turn off the GFCI and unscrew the light. There is usually a single screw that will release the entire light assembly. Pull it out and take it out of the pool.
Dry off the outside of the light and open it. If it is wet inside, there is a leak. Either the lens is cracked, the gasket is shot or someone didn't put it together right before installing it. Whether it is wet or dry, remove the ball and carefully run a cloth around the inside to remove any traces of moisture. Sometimes, just a little bit of moisture inside can cause the GFCI to trip even if nothing is there isn't a leak.
Replace the light bulb and the gasket. If you see a crack in the lens, replace it as well. Carefully reassemble it to make sure that it is water tight. It is always a good precaution to replace the gaskets when you replace pool lights.
Screw the light into the bottom of the pool. Make sure that everyone is out of the pool and turn back on the circuit breaker. If it goes on and stays on, everything is safe.