Just a note about the two bolts "under the armrest" that some folks have been explaining above. Our 2000 Blazer 4D 4WD LS has the rear door panel bolts in a different spot. Looking down at armrest, look inside the the grab handle. You'll see a ~3" long x 1/2"wide cover. Use a small flathead screwdriver to carefully pry up the cover from the rear end. Once the cover pops off, you'll see two 7mm hex head bolts. Remove these. Then follow everyone else's instructions to carefully pry off the door around the edges.
Also note, I had to remove the two trim pieces on the top half of the door before the lower panel could slide up enough to come off. The front trip piece is attached by two small phillips screws that are easily visible. The rear trim piece has the same attachments as the lower door panel. Carefully pry off from the bottom. Once the lower one pops out, you can just swing the trim piece up and out of the way.
The power window button is tricky. Once you get the trim panel off, spin it upside down so that the switch is facing downward. Use a normal sized flathead screwdriver to the pinch (wedge) the silver clasps towards the switch. The switch will pop loose and one of the silver clasps will go flying. Be careful that you don't lose it. Try to keep the other clasp in place so that you can see which direction they go.
My eventual goal was to replace the speakers. There's a GM spaker connector that is tough to disconnect. My best advice after I finally unhooked it is that you have to try and squeeze all four sides at the same time. Good luck.
The speaker had four 5/64 (I think) stardrive screws that had to be removed. Lastly, I have no idea what GM was thinking, but the hardest part is sliding the connector under the housing that holds the speaker in place. The housing is attached to the door by what looks to be four rivets. Dumb design. You'll know what I mean when you see it. Yes, I could have cut the wires, but I was hoping to easily re-use the connector on the new speakers. Nonetheless, I finally used a larger flathead screwdriver to pry the housing away from the door. Eventually the top left rivet-like attachment popped out and the connector slid under the housing easily. Am I going to be able to pop the rivet back in? Will find out later. If not, looks like I can drill out the rivet and use a sheet metal screw.
Hope this helps.