There are three screws that need to be removed, all on the armrest.
There are two large ones in the inside (toward the middle of the car) of
the armrest. Look for holes in the fabric, or buttons covering holes.
There is another small one under the top of the door closing handle
part of the armrest. All are Phillips head screws.
Then remove the plastic part that surrounds the door lock knob by prying
upwards on it. Do not neglect this last step.
Once these are removed, you can remove the armrest. Then loosen the
snap fasteners around the sides and bottom edge of the door panel by
just inserting your fingers and tugging sharply.
Watch out for the plastic piece that holds the top of the door handle
part of the armrest. It protrudes into the armrest (and through the
door panel), and you have to pull the armrest and the door panel clear
as you slide the door panel upward to unhook it from the frame. These
little plastic pieces become brittle with age, and like to break off.
Thanks to Egon Frech for this answer.