You need to ground the wire attached to the wrist strap for it to be effective... You would usually do this by connecting it to a ground off the mains supply in your house or building, your house/building is usually tied to either/or a long rod nailed into the ground or a buried metal pipe like your water supply line... And likely a backup ground from the electric pole in many cases... You can also common ground yourself to what you are working with, you will see many computer guys do this they just attach the strap to the computers case... IMO not the best practice especially if the computer is unplugged and not grounded itself, but better then nothing...
Best to ground directly to the house as I said, but sadly many homes are not properly grounded so you would need to verify any connection made... In the US the quick and easy is to back the screw out that holds the cover plate over the socket and attach a ground wire there with a crimp ring connector... But, this only works if the socket is properly grounded to begin with...
