The fuses in your VW fusebox are rated for amps. If too many amps flow through the fuse, it will melt and interrupt the circuit. To add a new circuit to your car, you only have to add one terminal to the back of the fusebox and one fuse to connect that terminal to the power bus. The new terminal goes to whatever you want to power.
A mk5 Jetta is shown but other models are similar. This article only shows how to add a fuse to the cabin fusebox. There is another fuseboxes on top or next to the battery.
The correct terminal size depends on the fuse. Here is what a VW
terminal looks like. There are metal tab-hooks at the top and bottom which
also hold the end in place. To release them, push a terminal release tool
or equivalent from the front to press the hooks down. Then it can be
wiggled straight out. Sometimes you have to push them in a little before pulling out because the hooks are dug in. When you insert a terminal, push it in until you
hear or feel it click. Gently tug the wire to confirm that it's
hooked. Once you're done, push the pink plastic back up and it will click
and lock the terminals.

You can order these terminals from the dealer but I get them from the junkyard. I have a few wiring harnesses left over from various projects so I reuse the wire ends. This can be confusing since the wire color changes but a multimeter can verify which wire goes where. I believe that exact terminal shown above is VW# 000 979 225.
Here are a few common terminal ends.
VW# 000 979 225 (2.5mm, shown above)
000 979 227 (2.5mm but with wider head)
wide heads:
VW# 000 979 135 E (1.0 mm)
000 979 227 E (2.5 mm)
000 979 306 E (4.0 mm)
000 979 407 E (6.0 mm)
Here is a link to a pictorial page of terminal heads
and what terminal head goes to what plug
Parts
10mm socket
T20 torx screwdriver
Procedure
Make sure the driver's side door is unlocked and the driver's seat is all the way back (more important if you have power seats).
Open the hood and remove the battery cover or flap. Use a 10mm socket to loosen the nut holding the negative terminal. You do not have to remove it all the way. Lift the terminal and secure it to the side.
Remove the headlight switch by pushing the knob in and turning it clockwise. Once the catch retracts, pull the switch out. For more details, see 1000q: headlight switch removal and euroswitch swap.
Insert a pry on the slot of the fusebox cover and pull. It has a few
snaps as seen below. Remove the 2x T20 torx screws indicated below. The fusebox is now loose but to access the back you have to remove the trim
around the headlight switch.

Remove the two T20 screws on the bottom. Telescope the steering wheel
all the way forward. Pull the trim underneath the
instrument cluster straight out and there's another T20 there.


Remove the T20 under the headlight switch and the trim will come out.
Unplug the interior dimmer as it comes out.


Remove the 6x 10mm bolts indicated below and gently pull the metal brace out.

Here is the brace removed. There is a clip at the back which looks like
it's at the bottom in this picture due to the perspective.

If you have the storage cubby under the headlight switch, you must remove it first before removing the trim. Here are some notes from digitalextremes: The change cubby can be removed by opening it fully, you can squeeze it from the sides when open and pull open further down, then pull from the bottom straight towards the back of the car and it will come out.
You now have plenty of room to work with the fusebox. Remove the rear cover by prying the plastic clip slightly to release the cover.

Now unlock the terminals. There are hooks that hold the pink to the black plastic. Pry the black plastic away from the hood at the arrow indicated below. It was hard to get a clear picture but it's obvious once you know to look for it. The push the pink plastic down to unlock the terminals.

Here is a terminal added to position 17. The blue/white wire is in the position
for the rain-light sensor and took a 5 amp mini fuse. Make sure that the
bus (each line of fuses) has a contact going to the spot you want to add the terminal. Some
buses are on all the time, some are on when you turn the car to ON, and some are
only on when the engine is running. You could add the terminal to any open
spot on the bus but it could confuse the next person who has to figure out what
goes where. If you do that, at least add a label to the inside of the
fusebox cover.

Here is a picture of the front of the box (ignore the labels, they are from
another writeup). You can see that some slots don't have any connection
from the power source. For example, spot 17 has a connection (the upper
half) where a terminal can be added to the lower half, but spot 18 does not.

Installation is the reverse of removal. The bracket and trim pieces have some play so I suggest starting the threads on every bolt before tightening any down. This also helps avoid crossthreading.
If you have any more questions about adding a circuit, feel free to ask in the forums linked at the top or search below: