First of all, you will need a soldering iron, solder and flux. It also helps trememdously if you have an extra set of hands to help hold everything together while you do the soldering. The biggest part of the job is not actually the soldering, but fitting the bridge to the fiddle. If you haven't done this before, I strongly recommend that you let a professional do this. Since the pickup is embedded in the bridge, if you mess up the bridge, you are done. My instructions here are going to focus on the soldering part of the job.
Make sure that you do the soldering part away from the fiddle. You don't want to accidentally drop hot solder on the instrument!
Start by putting the "cap" from the 1/4" jack onto the wire. Make sure the threads are facing towards the jack and away from the bridge.
The following picture shows how there is no solder or wires on the outside of the prongs.
When you are done with all the soldering, you can install the bridge with the wire facing the tailpiece. Install the jack on the same side as the chinrest. Screw the cap back onto the jack. It may look like the cap is not screwed on all the way because there are more threads on the jack than are on the cap.