You can either make a homemade soda (I have a ginger ale recipe posted) or do the water/extract mix. Sprecher Root Beer extract is a winner, but more expensive than the Gnome and McMormick types.
Mix it up. Put it in the kegerator at 30-40 psi, and it should be carbed up in a few days. To serve at that high psi, you'll need about 25' of 3/16" line. I just coil it around the keg.
Root beer will NEVER come out of the keg or the lines, so I have one keg for rootbeer and one super long line for it.