Inductive Charging Mouse
Do you want to do everything from scratch or rather use a prebuilt set that you just need to hook up? 

If you want to build from scratch take a look at this guide from 2007

If you want to use a prebuilt set (recommended) something like this could work:
Seeed studio wireless power supply  

or from Adafruit product 1459, as mentioned in the comments above.



but again consider that the 3.3V you get from the receiving coil can not be used directly to charge your battery, otherwise it will get killed, heat up or catch fire eventually. 

But closely take care of exactly how you charge your battery. NiMH and Lithium batteries require different charging voltages and currents. You have to add the correct charging device between the receiving coils voltage output and your battery. Just hooking up the 5V output of the receiving coil will destroy your battery and mouse!
Possibilities for NiMH batteries would be using a BQ2002 chip from TI:  Here you would have to make a small circuit board. 

Or if you are using a Lithium rechargeable battery a small prebuilt charger like this would do: 
From sparkfun: product 11231  (sorry i can only post 2 links, so please google the product)
From adafruit: product 1944 (sorry i can only post 2 links, so please google the product)