This may not be the best way to clean a device that this happens to, but it's how I did it. The other day I went to play around with my night-vision goggles. When I flipped the on switch nothing happened, so I assumed the batteries were dead. When I opened the battery compartment to replace them I saw it. That nasty yellowish gunk that means the batteries burst.
(BTW, this is entered in the Craftsmen tools contest!! I don't have any tools except the bare basics and it's really limiting what I can make. If I won I'd be able to bring you lots of cool stuff!!)
Step 1: Gear and Tools
First picture: Work gloves, safety glasses, screwdriver set (here is a good set: http://www.craftsman.com/shc/s/p_10155_12602_00904107000P?vName=Hand+Tools&cName=Screwdrivers&sName=Screwdriver+Sets&prdNo=1&blockNo=1&blockType=L1 , pocket knife, and multi tool. You should also wear a dust mask or better.
Second picture: Wet paper towel and dry paper towel.