I stumbled across these instructions on another site and they worked great for me. I had it replaced in about 15 minutes. This is for the inside door handle. 1. Remove the small screw holding the plastic trim bezel at the inside door release. Slide the trim towards the front of the car. If it is the drivers side, that would be to the right viewed from inside the car. If it is the passenger's side, it would be to left to free it from the door. 2. Disconnect the rod from the door handle and remove the handle. Before attempting to disconnect the rod, note that the retaining clip can be released from the rod and pivoted out of the way. The rod then lifts free.
Then it's a matter of putting in the new door handle\trim by inserting the rod into the hole and then pivoting the retaining clip back in place so it locks the rod. Then slide the handle/trim back in place and put the screw back in.
These instructions work for a 2001 Prizm LSI with power windows and door locks also. I would suspect the 1998-2002 would be the same, but I can not confirm that.
The only thing that disappointed me was I ordered the incorrect color trim off the internet (bone instead of brown) but hey it works great now! Check on Ebay for door handles. Big savings over the dealer pricing.
Edit: The person who wrote these instructions is exactly correct -- it worked perfectly on my Chevy Prizm 1999. Thanks to the author.