Do they still bury students in avy courses? seriously, do they? My avy training comes from the 60's at Alyeska taught by the Forest Service Snow Ranger; so it is WAY out of date. They would co lapse a snowbank over us to see what it was like and let us be the dummy victim. You people all probably know this stuff and better, but some reader may not have so suffer.
As old as some of this stuff may be a lot might be real pertinent to a resort skier without equipment. Even more useful if you are the one along for the ride. It will not work in all avalanche types, and some may not work at all. 55+ years of skiing some pretty snowy places, I have gotten to try a number of these ideas, and going skiing tomorrow.
If you are caught in a slab slide like this video there were a couple things that can help. Try to swim up the hill in the slide; helps keep you on the surface. If buried put your arms in front of your face; as motion slows down move your arms head and upper body as much as you can (you are creating as large an air pocket to breathe as you can, this may save your insurance company a lot of money). Breathe slowly!
If you are a searcher get yourself to someplace as safe as possible, you don't need to be another victim. Follow, with your eyes, as accurately as you can, the path of one person; that will be your target. After the snow has stopped ski down below your target, throw something up where you believe the target is and start your search. When the target is located dig from downhill of the target; easier to move snow down then up, and you are not reducing your victims air space. If you do not have a shovel you can dig with the edge of a ski, not as effective but often better than hands. From here, if all went well, it is just first aid.
Again this is from the Dark Ages of snow science. There are much better current Scorsese of information on this topic, but you have to go find it and you should. Rule one still applies; "DON'T PANIC".
Okay let the experts debate again, I am going skiing. Hope that you never need any of this.