What is the proper technique to self-arrest and brake a fall, given steep icy(frozen snow) slope, when wearing crampons and wielding an ice axe? Should the crampons be used for stopping or held high in the air, to avoid tumbling over them?
You never want to stop yourself with the crampons because they are liable to catch, flip you over, and at best, put you in a worse situation than before, and at worst, break your legs.
Instead you want to first stop yourself using the pick of the ice axe, with your crampons raised above the ice. You can use your knees as an additional brake. The way you do this is first get into self arrest position, which is face down, with legs downhill, one hand on the head of the axe, and one hand down the shaft, with the head on level with the shoulder. The pick is placed into the snow, and the bottom of the shaft raised, with the bulk of the torso placed on the shaft and and pick.
After you are stopped, or sufficiently slowed down, use the crampons to kick steps into the ice, and get yourself into a secure position.
It is highly recommended to practice this with knowledgable mountaineering guides or instructors on relatively safe slopes.