Disclaimer: If you mess up your stuff, it is your fault!!!Not mine!!
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
Lets not forget safety. You will be doing some minor scraping with possibly sharp 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.
Step 2: First the Easy Stuff
First get all the easy to get to battery contacts. The way I cleaned them was to scrape off the battery gunk as best I could, then wipe it with a damp paper towel, and lastly dry it off with the dry paper towel. Be careful on any springs, as you could bend or break them. I was going to use the knife or multi-tool blade to do the scraping, but I went with a flathead screwdriver instead.
Step 3: Now the Hard Part
Due to the design of this device to access all the battery contacts I had to open up the whole battery pack. Fortunately this was easy on this device with just four screws, none of them hidden. I used the same scrape, wipe, dry technique here.
Step 4: Put It All Back Together
Well, as the title says, put it back together!!!