Unplug the lamp
Remove the bulb
Remove the lampshade if needed
Open the lamp base or socket housing
Take a photo of the existing wiring
Disconnect the old cord from the socket and switch
Remove the old cord from the lamp
Cut a new lamp cord to length if needed
Strip the outer jacket and wire ends
Thread the new cord through the lamp base
Connect the hot wire to the brass terminal
Connect the neutral wire to the silver terminal
Reconnect any switch wiring as originally configured
Tighten all terminal screws
Secure the cord with the strain relief
Reassemble the socket and lamp base
Check that no bare wire is exposed
Install the bulb
Test the lamp after plugging it in
Stop and consult a qualified electrician if anything is unclear