You can use this just like a laptop's touchpad for the most part, albeit with an obviously smaller surface. Drivers/apps are available for both the Mac and Windows versions of this device. The black one is targeted at Windows, and the white one at Mac OS X users/computers, however they're the exact same thing. If you have the black/Windows mouse but want the app/drivers for Mac OS, use the T631. If you have the white one and want drivers for Windows, find the downloads for the T630 (this one) on the Logitech website.
There's a switch on the bottom that you can toggle left/right to tell it to which paired machine you should be sending input from that mouse. Pairing works the same way - just shift the switch to the left, pair it, then to the right and pair it with another device (computer, tablet, etc.). Then to toggle between those devices, just flip that switch.
You wouldn't be able to use this while charging because the only port into which you can plug your MicroUSB cable to charge is on the bottom of the mouse, below the laser used to track object movement.