Volkswagen Key Disassembly
In order to replace the battery on a Volkswagen Key you first need to disassemble your key. This takes a bit more force than most people are willing to do, for fear of breaking it.
Here is how to replace the battery and how to replace the metal bit that attaches to your keychain.

Grab the key with a firm grip on each side and simply pull very hard.

The key will separate into two halves.

This is the key slightly broken apart so you can see where the seam is.

Step 2 is a little harder. Get your finger nails between the two halves. Either grab from the front or sides and pry hard and it should pop in half again.

Successes, now the battery.

The battery is pretty simple, pop it out. Although I prefer to pry it out with a small jewlers screwdriver as shown.

Battery Type: CR2032
Replace it with any brand CR2032 you like.

Broken keychain? No problem!
The dealer will claim you need to replace the entire key...aka... $$$.

Note how on the two halves of the back side of the key the electronics are on one side and the keychain is on the plastic bit with the battery.

Simply ebay the cheapest key you can find (should be <$15) and grab that plastic bit off of it. Save yourself the time and money of getting a new key and having it reprogrammed.