How do you replace the battery on VW Jetta 2003 alarm?

I assume you mean the car key with the flip button.

step one: Yank it apart, grab both ends and pull longways until it comes apart.

step two: Pry the bottom part in half with a screwdriver or butter knife.

step three: You should see the battery now, take it out and take it to a drugstore/Walmart and get a replacement.