Here's a pic of the switch I stole from some car parts site on the web
The switch is (or in your case, was
) attached to the bezel, or trim piece, by three screws. You can see the attachment holes in the pic. It is theoretically possible that the screws came undone, but that's very unlikely. More probably, those little plastic hoops for the screws broke off.
The trim/bezel isn't that hard to take off, but it is important to do it the right way. The end nearest the front of the car has a friction peg that goes into a hole in the door trim, the side nearest the rear of the car has a clip that goes under the edge of the door trim. Here's another stolen pic marked to show the clip and peg.
To take the bezel off, use a screw driver, knife, or some such thing and pry up the top, the front edge nearest the front of the car, and when that is up enough to free the friction peg from the hole, slide the thing forward to clear the clip. If you pry up the back end first, the side nearest the rear of the car, you'll break the clips and the whole trim bezel will flop around. After its free from the door panel, there's one electrical connector to disengage to fully free the thing from the door.
Once you get the bezel and switch off, you'll be better able to see what's wrong. If the plastic screw loops are broken, you may be able to rig some hack to hold it in place, or it looks like you can get a replacement online for under $30. Its also possible that the switch is fine but the holes that the switch screws into are broken, in which case you'd probably need a new bezel. 03-08 Toyota Matrix switch and/or bezel will work in your 07 if you can't find a pontiac vibe one.