The battery in an Audi is not in the most obvious place; there are very specific steps you must undertake (different from most other cars) in order to replace it. Batteries in an Audi normally only need to be replaced under one of two conditions: the alternator fails or extreme weather saps the electrical charge.
Remove the weather stripping on the firewall. Grab it with your fingers and start tugging at it and it will pull off the firewall.
Remove the plastic shield covering the battery. This is held in place with two metal clips that you will have to pull off.
Unbolt the cable from the negative battery terminal first. To do this, loosen the retaining nut on the cable clamp counterclockwise until the clamp is loose enough for you to pull it off the battery terminal. Then, loosen the cable attached to the positive terminal and remove it.
Unscrew the battery wedge with the #6 Allen wrench and slide the wedge out of the way.
Remove the breather tube from the battery by pulling it off.
Tilt the battery backwards, and then pull it out of the engine bay.
Install the new battery. Installation is the reverse of removal.