as I understand it, you put them on with adhesive.Some do, some don't. One of my favorites, the pad made by Oracle, uses an adhesive.
The function of the mat is to control resonance generated in the vinyl by the act of the cartridge tracking. If you can hear the cartridge tracking the vinyl with the volume all the way down, that's a bad sign, and also a way to let you know how effective your mat really is. The mat should also therefore be able to damp the platter as well.
If the mat is too hard or too soft, it will introduce a coloration. The correct durometer is that of the vinyl itself. This is why felt and metals both do not work right, although felt is often used because it can act like a clutch during DJ work.