This page was taken from Ken Chan's Neon page with premission from the owner.
Here are a few simple instructions on how to remove the door panel to access the speakers, and window components.
The first step to removing the door panel is to remove the window crank. There is a special U clip that holds the window crank unto a groove on the window crank shaft. You must remove this clip before you can do anything else on the panel. This clip can be easily removed as shown with a door handle removal tool, or with a very flat screw driver or piece of metal. Once this clip is removed then the door window crank should come off easily. Next you must remove two other screws. One is in the door pull cup (may look different on other neons, I know mine is facing up not back) and the other is behind the latch release handle. The one in the pull cup requires a screw driver, but the one in the door latch release handle requires a torx bit. Once these three things are removed, then the panel may be removed by pulling the edge of the panel out from the bottom of the door. Work your way around and up. You may then lift the panel slightly to remove it from the top of the door. Next you have to unclip the rod that connects the door latch to the door latch handle. You should now be able to remove the panel completely.