Attaching the plug to the cord is even easier. Squeeze the prongs together to pull them out of the plug's case. Pull the prongs apart and insert the free end of the lamp cord through the small hole in the back of the case and between the prongs. Each prong has a sharp metal bit that should pierce the cord's insulation and make contact with the copper wire inside. (One of the prongs will be a little narrower than the other. This one should pierce the marked side of the lamp cord.)
If you're having trouble, nick the cord with an X-acto knife to ensure contact. Reattach the case by pushing the prongs back in.