You will need to detach the pump from its bracket before taking the bracket and top of the plunger firmly in one hand. With your other hand, grip the pump in the center and apply pressure toward the handle of the pump. Begin to twist the pump clockwise. It will break free so you can unscrew just the plunger mount with you fingers.
This can be done easily by applying some lubricant to you finger then rubbing it on the o-rings on the new plunger. You may also wish to apply some to the threads of the plunger, but this is not necessary. I've used clean motor oil on the grounds that this pump generated quite a bit of heat during use. Also, it was the oil closest to the doorway I was standing in.
If you can't figure this out, just buy a new one, you dolt... nevermind. This is actually hard as hell! You are not a dolt and I'm sorry for having flown off the handle like that. Anyway, take a pair of pliers or vice grips and lightly apply them around the disk of the plunger. Then, twist the pump counter clockwise (or the disk clockwise, but this is difficult).