MOst likely is that the switch is set to "off". On many GM vehicles, it's on the headlight switch. If you have owner's manual, look in there, if not google it. If not the switch, next check the fuse, then bulbs, then door jamb switch.
On most cars the overhead light has three positions - always on, door activated, or always off. Can you get it to turn on manually? If so you know the bulb is good - then you either have the switch in the wrong position or the switch in the door jamb has failed.
Open the other doors to see if they lights come on. If they do likely the door ajar switch is bad. If the lights don't come on. Like said above the fuse or bulb(s) are burnt.
Fuse or wiring. There might be a button on which the door closes. It holds the button down when shut, turning the light off. The button could be stuck down. Did you try the other door(s)?
Burt bulb, blown fuse, or wire short; in descending order of likelihood.
turn them on before you get in. that may be the problem.
...when i open the door, the lights wont come on. I have a 96 Buick, what could be the issue?