Flick all of the light switches in your apartment. Do they work? Make sure none of them appear damaged or have loose wires hanging out. Each switch should have a faceplate as well.
If the lights don't go on, check the bulbs. Usually, you're responsible for changing those in your apartment if they're burned out. Obviously, the lights shouldn't flicker or throw sparks either. Also, you'll want to plug a small appliance (or an electricity tester) into each of your outlets to make sure that they all work.
Open up the fuse box if your unit has one. It shouldn't seem damaged or look like it has switches missing. If the fuse box has more than one 30-amp fuse, the box may be overloaded, which could present a fire hazard.