Shortening the Rope:
With a figure-8 tied to the harness, pull tight on the rope and tuck under left arm, around and over right shoulder. Place left thumb through belay loop and fingers outstretched as shown in  and coil rope under fingers to over and around right shoulder as many times as needed until the rope to your partner is the desired length. Keep the coils tight. The palm to shoulder spacing is imperative and ensures that the rope doesn’t strangle you (if too tight) or slide around and off the shoulder (if too loose). Once the rope is the desired length grab the coils together in the left hand as shown in .
With the right hand make a U (a bight) and pull it through the loop caused by the figure-8 follow-through and the belay loop as shown in  below. Put your left hand through the coils and pull the bight through them from the strand going to your partner.
Tie an overhand on the strand going to your partner as shown in  above. To redirect the strand going to your partner more through the hip belt you may clove hitch the rope going to your partner into a locking carabiner in your belay loop. During glacier travel always keep a prusik knot (roughly 5 feet long when untied) tied into the rope going to your partner. Clip the other end of the prusik loop to a locking carabiner and attach that to your belay loop [also seen in use in 5 below].
Make a T-anchor with a picket and a locking carabiner in the middle hole which is exposed by the trunk of the T. Run a double length sling out of the carabiner. Clip the carabiner attached to your prussic knot into the anchor (double sling) as shown in  above, where a rock anchor is used instead of the described picket / sling system. Always leave locking carabiner gates facing upwards for easy load / unloading. Check if the fallen climber is capable – they should ascend out of the crevasse via prusik and a Garda hitch or alpine clutch (see addendum A) on the main rope, instead of the other climber lowering themselves to pull them out. If not, follow the steps below.
Release and uncoil the rope by raising the strands one by one over your head / left shoulder and dropping them in a pile akin to flaking them. Attach the uncoiled strand to another locking carabiner attached to the anchor sling via a clove hitch as shown in . Pass that strand through your belay device attached to your belay loop. You will rappel down this strand shortly. Before rappelling, attach a short prusik loop with the knot into the strand of rope between you and your rappel anchor. Attach the other end of the loop into a locking carabiner (separate from the one your belay device is attached to) attached to your belay loop. This will act as your harness loop on the way back up. If the fallen climber is conscious, and able, they should screw in an ice screw and attach themselves to it, as a backup to the anchor.
Lowering into the Crevasse to Investigate:
Place an ice axe on the lip of the crevasse to reinforce it or “prep the lip”. When placed correctly, your rappel strand is going to lie over the axe and that will keep your strand from digging into the lip of the crevasse. Attach the ice axe (possibly using a draw / sling) to the original weighted line going directly from the fallen climber to the picket/anchor. This keeps the axe from being knocked off into the crevasse. Drop the loose coils (the end of which is tied to your belay loop via the figure-8 follow through) into the crevasse and slowly rappel down the strand attached to the anchor, un-weighting the prusik and moving it with you as you lower yourself to the level  of the fallen climber via the anchored rope marked by the blue arrow. Once down at his / her level, make an overhand on a bight in the brake strand downstream of your belay device to act as a backup for yourself. Now attach one of your partner’s or your locking carabiner to his / her belay loop and pass the rope strand downstream of your overhand on a bight through the carabiner you attached to his / her belay loop. Take pains to avoid the insidious evergreen bushes seen in  and  that shamelessly lurk in the shadows of the deepest crevasses, waiting to devour the unsuspecting fallen climber. Now you are ready to begin ascending the rope. If needed you may use a double length sling together with prusik cord to attach a chest harness to your partner. A chest harness may be needed if he / she is unconscious.
Re-ascending the Rope:
Place a garda hitch or alpine clutch (see addendum A) on the rope between your belay device and your harness prusik loop. Girth hitch a very short leg loop to the base of the carabiners used for the garda hitch. Place your leg in the leg loop  and stand up on it, un-weighting the prusik loop attached to your harness. Move your harness loop up the rope as far as you can. Yank the strand downstream of the garda hitch upwards. If set up correctly, the garda hitch results in the biners moving up while their downward movement is arrested. Now you are ready to stand up on the leg loops again and repeat the process with the harness prusik until you are past the lip of the crevasse. Once back at the anchor, begin hauling in the rope that you ascended . When hauled correctly you will feel your partner at the end of it once all the slack is taken up.
Setting up the Pulley System:
Place a belay device into the anchor sling using a locking carabiner (gate faces up again). Pass the strand of rope that comes from your partner through the device as in . Attach a short prusik loop close to the belay device as shown in . Pass the loop of the prusik knot through the carabiner holding the belay device. This system acts as a “progress capturing device” that captures and holds all the slack (progress) pulled through the pulley system upstream of the belay device. Now attach a third prusik loop to the same strand of rope, close to the lip of the crevasse as shown in . This loop may be very small. If the loop is large, shorten it significantly by tying an overhand knot. Clip a carabiner through the now shortened loop and clip the rope coming out of the belay device through this carabiner. This system is called the ‘tractor system’. The strand downstream of the carabiner is what you will tug on. As you can see in , the progress capturing device’s prusik tenses up and holds any of the hauled rope upstream of the belay device.
Extract Your Partner:
Lean away from the tractor system pulling the strand emerging out of it. The tractor moves in position towards the belay device  as marked by the red arrow. Reset the position of the tractor, pushing it back to the lip of the crevasse each time it arrives close to the belay device. Continue hauling until your partner is out of the crevasse. It may be necessary to clean hanging ice off the lip of the crevasse before hauling your partner through. If it feels as though the rope is stuck, go and examine your partner. It is possible that his / her further progress is being hindered by ice overhanging the lip of the crevasse.
Random Trivia: AMGA certification requires execution of the above activities in 45 minutes. Piece of cake? Consider the worst case scenario that these maneuvers may be happening in a whiteout and temperatures of -40F.
Garda Hitch or Alpine Clutch: http://kurthicks.com/2011/08/07/garda/
It is important to use two carabiners of the same size, both oriented in the same direction. Pass the strand of rope through both gates of both the carabiners. Loop the rope around behind both the carabiners, bring it back around to the front and clip it into the top carabiner (i.e. the carabiner closest to the direction of ascent). Girth hitch the bottoms of both the carabiners together with a loop to use as your foothold. Yank the strand of rope downstream of the garda hitch to move the system upwards.