My wife and I have wireless mice on our different computers.
What generally happens is that there is some sort of receiver which is plugged into a USB port on the computer somewhere (it doesn't have to face front necessarily).
The mouse itself generally has a couple of batteries ranging from AA's in the larger rodent (probably ought to be renamed to a rat!) to AAA in my 'notebook' version which is tiny.
Have a look at Belkin, Logitech and Microsoft. They are more or less similar but often have slightly different 'bells and whistles' it's really a matter of personal taste.
If you've a branch of PC World nearby you can actually look at one physically, but they are cheaper on line usually.
I've been using one for about 2 years - I'll NEVER go back now. Might I suggest that you invest in rechargeable batteries (two sets is a good idea too for when they run out).
It's Sod's Law that the batteries give up the Ghost when it's least convenient.
Hope that helps.