Most standing lamps consist of a body, a base where the cord enters, a harp to support the shade, and a socket, which receives the cord at one end and the lightbulb at the other. The cord usually runs through a hollow threaded rod from the base to the socket.
When a lamp won't work and you know the bulb is OK, check the cord for damage. If the insulation is worn and cracked, replace the entire cord (see Rewiring Lamps, Related Projects). If the cord is OK, the problem is most likely in the socket.
Most lamps have felt bases that must be removed before repairing the lamps. Remove the felt by paring it off with a utility knife. After the repair, reapply the felt with white glue.