Here is the hole left with the wheel speed sensor removed, giving you just enough room to work with in getting the old stud out and the new stud in:

Rotate the hub such that the stud is in line with the space you created by removing the wheel speed sensor. Make sure the ring is slid out of the way before you go all Captain Smack-a-Hoe on the stud. Be patient, the stud will come out with continued persuasion. Using your telescoping magnetic grabber thingy (TMGT), fish the old stud out.

Time to rotate the hub again:

This is the hub position that I found to cause the least amount of cussing while trying to fish the new stud into place. Go grab your new stud from the freezer, and fish it into place using your TMGT. This can take some creative use of fingers stuck into small places, but you’ll get it eventually.

Using your Home Depot Racing washers and a lugnut, pull the stud into place by slowly tightening the lugnut. With the frozen stud, this should not require a ton of force. Just take it slow, and continue until the stud is fully seated (easy to check visually).

And now to reassemble, in the following order:
-ABS ring
-ABS Sensor
-Rotor: Double check that the rotor is FULLY SEATED before continuing! Use a block of wood and a hammer (or a hard rubber mallet) to fully seat the rotor. If the rotor isn’t fully seated you will have problems with the next step.
-Caliper
-Wheel
-Test Drive!