You can stop by your local hardware or hobby shop and pick up a new lamp socket for just a few bucks. I usually have a couple of spares laying around for when i need them.
You can see in the image how only a few parts make up the main socket. Start with screwing the entire socket off. This can be tricky some times because it involved twisting the cable as you screw it, which starts to build up tension. Just be careful not to over-turn it. Then the bottom cap pulls right off (some times its a little snug). Then all you have are two screws holding the wires in place. MAKING SURE THE WIRE IS NOT PLUGGED INTO THE WALL, you can unscrew them from the old socket. Replace a new socket making sure the ribbed wire is connected to the negatives screw (most times the positive screw is golden, just check before you remove them from the old socket).
Once the wires are securely fastened on the new socket you can replace the cap on the bottom and put the rest of the lamp back together.
Easy and Cheap way to fix any lamp in your house.
I have uploaded two illustrations found online that provide a quality break down of the parts.
Original Illustration Credits: