With a volt meter check to see if you have power to that socket. Check at the wire not the socket. If you find you have power, either the socket is corroded or broken. Also check the ground connection at that socket.
a bulb is bad and must be replaced
Either check the fuses or change the bulb.
You have a broken wire.
my Oldsmobile alero did the same thing. It turned out to be as simple as a blown bulb in my tail light.
I just had the same problem and found that my rear turn light bulb went out and the turn signals no longer worked. Check any of the turning bulbs. You may have replaced the hazerd light flasher. There are two flashers, the turn signal one is near the hazerd one under the dash.
A blown bulb. Check fuses and then start replacing the bulbs one by one.
Your owner's manual is the best place to locate your fuse box(es) and identify your fuses. Don't rule out that your issue is being caused by a bad bulb too - so check fuses and bulbs. See sources and related links below for bulb information.
A short somewhere in the wiring, an incorrectly installed bulb, damaged horn ring assembly, etc.
I'd first suggest checking to make sure that no fuses or relays have popped, especially if the car's battery was not disconnected when the bulb was replaced.
First check that ALL of your light bulbs are working for the signals. Some models will freeze operation of signals if a bulb is out to let the operator know that one needs to be replaced. Next check the flasher solenoid(s) near the steering column / brake pedal area. They are very cheap to replace. Also check that ALL of the signal sockets for the bulbs are in good shape. If they are burnt then it is the same as a bulb being out.
change the light bulb
You could have a bad bulb or loose bulb. Check out the reference page I am giving you.