Many people here know from my
web page on falling that my own approach to a broken leg was to spend a few thousand hours learning how to fall, until it doesn't scare me any more. (Not good - it meant I started trying stupid things like roller blading, and spinning and skating backwards on skis, which did cause some injury, though nothing as serious.)
But my response was extreme. After the cast came off, it took me another year before I returned to the ice.
The more balanced approach some of the people have here makes more sense to the serious skater. One of the ladies on this board wants to wrap skaters up in bubble wrap, which should make a very light and airy fashion statement. Roller blading, hockey and football outfits (which are lighter than hockey outfits) have also been suggested. If it gives you the confidence to keep skating, that's an incredible boon.
That said, it doesn't hurt to spend a few hours on falling, and to review it once in a while to keep the reflex speeds up -
once you have healed. Not all coaches have much fall training, but a lot do, so if you trust your coach, start with them. Master falls in all possible directions, out of all possible moves. Start low, sitting on the floor, and work your way up.
I also believe it probably helps to try other traditional injury reduction strategies, such as strength training (so your body can take more stress, giving you a larger margin for error) and flexibility training (if your muscles aren't long enough to give you an adequate safety margin - all my injuries are related to this issue), if they seem appropriate to you.
&) But your very FIRST step should be to move to a planet with less gravity! &)