Ummmm, very carefully? Just kidding. What I have always done is simply solder the new wire to the old wire, lubricate it with a little silicone spray and pull it through into the passenger compartment. Once in the passenger compartment you can either simply butt connect it to the existing white wire or if you have the correct factory terminal end, crimp it on and it will be just like factory. A blow by blow would be something like:

1) Remove passenger kick panel and remove single white wire from 3 pole connector.
2) Remove gear selector housing and cut zip tie that holds down white wire
3) Raise car up and pull white wire through rubber grommet in shift bucket until you have enough to work with. Caution, if you pull too much you will loose the wire under the carpet between the shifter and the center console in the passenger compartment.
4) Remove the housing on the female end of the white wire, cut the female end off and tin the wires (new one and old one), solder them together. Not too much solder and make sure that it is not jagged and will slide through the rubber grommet easily.
5) Spray it with some silicone lube or something, go back up to the passenger compartment and pull it on through. Pull it all the way through the grommet and under the carpet to right where you need it at the three pole connector.
6) Pull if far enough through that the length hanging out of the shifter and going to the trans is correct, not too long or too short. Cut apart the solder joint, butt connect the old male end onto the new wire and re-install it in the 3 pole connector.
7) Put a new zip tie on at the shifter, reinstall all your covers and panels, double check your length underneath and you are done.

It might take you a few to do the first one but once you have done a couple they are a snap. The real hassle is going under the car and back into the passenger compartment a few times back and forth, but other than that it is a cake walk.

Mark