Would anyone be kind enough to explain this procedure to me, a few basic steps for carrying it out and common pitfalls and just general hints when doing it, so that me and an instructor can go over it in a pool a few times.
Woodsie, it's a lot easier done than described. The tank cradle is a technique in which you are behind the victim and you hold his/her tank steady with your knees while you reach in front to manipulate his/her gear, primarily in order to establish positive buoyancy on the surface by inflating his/her BCD, and if necessary, reaching around to drop his/her weights as well. If you want to try it out in the pool, get a colleague (the victim) to try to grab you (the rescuer) on the surface with the intent of climbing up on you; descend to about knee level of the victim, swim around behind, and as you surface, grasp the tank between your knees, and then on the surface, inflate your own BCD and lean back to get control of the victim; reach over the victim's left shoulder to use his/her power inflator, and if necessary, reach around with your right hand to release the victim's weight belt.
Assuming a single tank back mounted.
It's usually practiced first in surfacing the unresponsive diver. (which is the code word to search for videos on YouTube.
I would not recommend the tank cradle for this sort of rescue. The rescuer of an unresponsive diver underwater does not need to cradle the tank with the knees. For one thing, when you've got an unresponsive diver underwater to surface, you are going to need to fin while you bring the victim up, and you cannot fin effectively while you're cradling the tank with your knees.
It's holding their tank between your knees with the diver facing away from you. Depending on what exactly you are doing, the right arm is over the diver's right shoulder holding the mask/reg in place, and the left hand is over their left shoulder operating their BCD. Since you do not have much kick available because your knees are locked on the diver's tank, you can use their BCD to control ascent.
The obvious benefit is that if the unresponsive diver (since that is the usual case for using it) suddenly becomes responsive, they would have a pretty hard time overcoming you since they are facing away, and you can get a pretty good pinch on their tank.
It would be nice to link a video on YouTube but they all show the rescuer putting their right arm under the unresponsive diver right arm, which pretty much loses most of the benefit of being behind the unrepsonive diver since that diver can get control of the rescuer pretty easily with the rescuer's arm in that position.
This is markedly different from the way I teach surfacing an unresponsive diver. Yes, I have the rescuer put his/her left arm over the victim's left shoulder in order to have access to the inflator hose, but this is mainly to DUMP air from the victim's BCD as needed as it expands so that the rescuer remains in control of the victim and the two of them don't get dragged to the surface by the gear. This doesn't mean there will be no air in the victim's BCD, but only enough to get both the victim and the rescuer neutral so that finning up with the victim is possible at a safe ascent rate (for the benefit of the rescuer, at least). I also teach putting the right arm under the victim's right shoulder. This provides not only leverage, but also goes a long way towards preventing hyperextention the victim's neck as the rescuer holds the reg in place and fins towards the surface.
If a rescuer were not finning because s/he was using a tank cradle hold and were holding the victim's body by the head with the right arm over the victim's shoulder, the rescuer would essentially be dragging the victim up by the chin, and as a result hyperextending the neck. The head should stay in a normal position while holding the reg in place rather than hyperextending the neck during the rescue.