So my closet light dies.

I have a light in my closet (simple, screw in lightbulb type), and the bulb blew out. Not a big deal, right? So I replace the bulb, and the light still doesn’t work. I have a feeling the socket has died somehow. I am electrically stupid. Basically, I know I should probably shut off the breaker and try and fix it. But is it something I should leave to an electrician? Or should I even try figuring it out myself? What would I look for?