If you happen to have a non-contact voltage detector, operate the door or turn on the light and stick it into the socket. If it lights, the follow the steps in the next paragraph. If you don't have a tester, just go to the next paragraph.

At the bottom of the light socket is a small tab that makes contact with the base of the light bulb. It's not uncommon for the tab to be depressed over time and not spring back. Unplug the opener and use a small screwdriver or I'll often bend the end of a large paper clip into a L shape about 1/4" long. Gently pull the tab up.

If the tester doesn't light, then you'll need to open the case of the opener and trace the wires that supply the light back. I've never looked but I assume they come off the control board.