If the lamp has an integrated plug on the end of the cord now, you'll need to cut it off and buy a replacement plug. The replacement may come with instructions. Is the existing plug a single 'blob' of plastic, or does it have some way of opening?

Besides the hecka annoying popups, there's a decent step-by-step on replacing plugs over at the Better Homes & Gardens site which includes pictures. One thing I didn't see explicitly called out on it is polarized plugs. The 'ribbed' wire in the cord should go to the wider prong on the plug. Also, the instructions mention a 'cardboard cover'. I seem to recall that's no longer allowed by code, but instead plugs are supposed to have a solid cover. But either way, don't forget to replace it :-)

Look for a replqacement plug that simply attaches without stripping.
The cap is slid over the wire, it is inserted into an opening in the body, then the prongs pivot in and pierce the insulation and make contact. The cap then slides down over the body and snaps in position.
The only thing you can do wrong is not put the ribbed side into the body to connect to the wide prong.