To rewire a floor lamp, begin by unplugging the lamp, and then turn the lamp on its side. Pry the bottom of the base off of the lamp to expose the cord and the nut that holds the cord in place. Twist the nut to the left to remove it, then grasp the socket at the top of the lamp and pull it slightly. Unscrew or pry off the old lamp socket with a flat screwdriver.
Purchase a lamp rewiring kit that contains a socket, a plug and a generous length of lamp wire that matches your floor lamp. Cut off the old plug and then pull out the socket completely to remove all of the old wiring. Feed a length of lamp cord from a rewiring kit through the bottom of the lamp and up through the top of the lamp. The lamp plug should be on the other end of this piece of cord.
Divide the cord for approximately 4 inches into the two separate wires using a wire cutter to split them. Strip approximately 1 inch of insulation off the ends of the wire. Use an underwriter's knot to secure the ends of the lamp cord to prevent the cord from falling into the lamp.
Attach the ends of the wires to the correct screws on the new socket, consulting the kit's included wiring diagram for more information. Reattach the socket to the base. Then replace the lamp nut to secure the cord, and reattach the bottom base of the lamp.