Camry install

Does the vehicle have power windows?  If not, then you'll have to remove the window crank in addition to those clips.

Now for the clips, the best way to do it is to wedge the tool in between the metal and the plastic panel and just put a little prying pressure on it and move it along the edge. You want to find where it gives you the most resistance--should be about every 12 inches or so, all around the perimeter of the door panel (except for the top part near the window).    Wherever it give you the most resistance is where the clips are and so you can apply a good deal of force to pry them out.

I personally like to use one of these tack pullers because they work well with these clips.  I usually try to pull all of the clips out of the metal door part at least, and then pop them back into the door panel that i just removed.  This way when it comes time to put the door panel back on, having the fasteners in place makes it easier for you to properly line up the panel with the holes in the metal door.

Here's the scosche directions for the door panel removal, in case you need them.:

1. POP OUT SCREW COVER AND REMOVE SCREW FROM BEHIND.

2. EXTRACT (2) SCREWS FROM ARM REST BEHIND COVERS.

3. POP OUT SCREW COVER AND REMOVE SCREW IN THE DOOR RELEASE

HOUSING CUP.

4. POP OUT TRIM/RELEASE CUP WHERE THE DOOR HANDLE AND LOCK

SWITCH PIVOT.

5. EXTRACT (2) SCREWS FROM BELOW DOOR PANEL MAP POCKET.

6. POP OUT INSIDE MIRROR COVER TRIANGLE AND REMOVE.

7. REMOVE POWER WINDOW SWITCH PANEL OR WINDOW CRANK:

WHICHEVER APPLIES.

8. USING A PANEL REMOVAL TOOL, CAREFULLY POP OUT FASTENERS

AROUND SIDES AND BOTTOM OF DOOR, LIFT AWAY, AND REMOVE PANEL.

9. EXTRACT (3) SCREWS HOLDING SPEAKER, UNPLUG SPEAKER AND

REMOVE.

Should look something like that.  The part at the top is how it slides into the holes in the door panel, and then it's kinda hard to tell in the picture but there's a little angle/bend on the bottom section and this is what makes it snap  into the holes in the metal door frame.