First, you need to remove the valve to make room for the jig to fit in. It's best to depressurize the keg as much as possible with a tap. If you don't have a tap, you can also push on the valve with a screwdriver to release the pressure. Warning: You may be covered in old beer if you try this as it will be shooting out the top.
There will be a retaining ring ( not pictured) just under the upper lip of the opening. You can pry this out with a small screwdriver or something similar. Grab it with a pair of pliers and get it out of that lip.
Now it just needs to be twisted counter clockwise a few degrees to come right out. Put your screwdriver on the tooth pictured and tap it with a hammer. This should twist it slightly, allowing you to lift the valve right out.