Here we go with yet another test of my descriptive/technical writing skills...
Rappel Rescue
OR
How to do it on top...
You will need to know: The Mule knot, the Klemheist knot, Prusik knot, and the Munter hitch.

Start with an autoblock on the leg loop of your harness, and a 48 inch runner girth hitched through the two tie-in points on your harness. Tie a knot in the middle of the runner and attach a locking carabiner below the knot. Place another locking biner on the free end of the runner, and attach it out of the way on your harness.

Escaping a belay that is connected to the anchor (but not you) is similar to the process described in the first article in this series.
First, back up your belay. Girth hitch a short cordalette to the leg loop of your harness, and with a Prusik or Klemheist, attach it to the belayer's end of the rope. This way if you let go of the rope at a critical point, the friction knot will catch it. (This is the same autoblock you'd make if you were rappelling solo.)
Then tie off the belay device with a mule knot. No need to wrap it below the ATC this time, since it's already locked off by the climber's weight.

Next prepare to unweight the belay device and transfer the load. Take a second long cordalette and make a Klemheist knot on the (weighted) climber's end of the rope, below the belay device. You will transfer the load to this cordalette while you remove the belay device from the system.


Without removing the rope from the ATC, attach it to the 48 in runner you prepped earlier, as if you were going to rappel on it (and you are...) Now clip the rope directly into, and remove the ATC from the master point.

The next step is to remove the Klemheist cordalette and rappel down to your climber. If you or your climber weighs significantly more/less, consider placing an additional Prusik between your harness and the climber's rope. This will prevent too much slipping as you move down the rope.
Double check that the rope is directly clipped into the anchor, then remove the long cordalette by undoing the mule knot and munter. Detach the Klemheist and take the cordalette with you, as well as any extra gear at the anchor.
Slowly rappel down to your fallen climber. Attach the free end of the 48 in runner to their belay loop. This will ensure you rappel at the same rate, keeping you together. If you tied a Prusik on the climber's side of the rope, undo it now. Take the cordalette with you.
Rappel in tandem down to the ground or next belay ledge.
Lessons:
Though a bit more complicated, this process uses a few basic elements: Always back everything up, never untie/unclip completely, and know your knots. Even if you can't remember the step-by-step, if you find yourself in a jam, some creativity and those core elements will help get you safely out.
Warning! The information provided on this page may be incomplete, inaccurate or outright incorrect. Use your own judgment when using the information provided here. Considerable attention and effort have been made to ensure that these descriptions are accurate. However, many critical factors cannot be controlled. No responsibility is accepted for incidents arising from the use of this material.
Ps. Go take a class!