An Apple wireless (Bluetooth) mouse?
For either the Mighty or Magic Mouse, see
Apple HT2845. Basically, turn it off, take out the batteries, put them back in, turn it back on, and after a 5-sec steady light, it should flash to indicate that it is in "discovery mode." This is how you initiate paring, so at this point you should have the Bluetooth Setup Assistant (System Preferences -> Bluetooth -> "+" button on lower left list) on the desired computer started and looking for the mouse now.
(In fact, you may want to remove it from the Bluetooth list on your first comptuer to prevent it from re-pairing undesirably when you switch it back on. I haven't done this often enough to remember.)