UMs haven't been that popular until recently so it's not a strange question!
There are two types of unmounted stamps...the real rubber stamps and then acrylic (clear) stamps. Both of these get stuck on to an acrylic block. With the clear that's it and you are ready to stamp.
With rubber you have several choices. My method is to use the ez cling (aka creative cling as TAC calls it but it's available alot of places). TAC sells its stamps with the cling right away but some places, when you order online, you may just get a slab of rubber! Other folks use double sided tape, carpet tape, or Aleene's Tack it Over.
There are many threads out there on the pros and cons of the different mounting methods. The benefits are that UMs are cheaper and take less storage space.