I just did this on my wife's car, and want the next person who comes along to have an easier time.
First, you'll want to make sure you have the proper tools:
First, remove the speaker cover. There's a slot at the bottom of the speaker cover that allows you to use a flat-head screwdriver to pry out. Inside, there are six phillips-head screws. Three hold the speaker to the door panel, and three hold this corner of the panel to the door. Remove them all, and disconnect the speaker.
Next, remove the three screws that hold the armrest. Be gentle with the armrest after removing these screws. Remove the screw behind the door handle. Now, look at the bottom of the door panel. There should be three clips towards the back of the door. Pull the door panel away from the door GENTLY to see where they are, and use the trim remover tool to pop out the clips.
Now comes the tricky part. First, you'll want to lock the door (while it's open) to make the door lock post (the little post that goes down when you lock the door) easier to navigate around. The door handle and lock button should slide forward about 1/2" (1-2cm for you metric folks). You should feel it come loose. Starting at the back of the panel, lift the panel up and forward, being careful to navigate around the door lock post. You may want to GENTLY help this process by prying up on the top, where the panel meets the window.
Once the panel is mostly free, you'll still have the lock button and door handle to deal with. There is a plastic clip that will spin to free the door handle from the pull-rod. Spin this clockwise to unlock it, then slide it up and out. Unclip the electrical connector for the door lock button, and that should be it!