Becoming a better skier depends to a large extent on mileage - quite simply, the more miles you put under your belt, the better you will be skiing. Combined with hints you can find elsewhere on how to improve your balance, you will be well on the way to skiing better.
Obviously, the high mileage you are clocking up from dawn to dusk on your week's skiing holiday will mean that initially you will be falling a lot more. This may be bad for your ego, but at this stage you must abandon any pretensions of being a good upright skier for the opportunity to become a good horizontal skier!
I mention elsewhere what Ian Fleming once said about falling over and this is during the same season that he took up the sport in 1928, but it is so important that it needs to be emphasised again: 'Surely it can't be difficult to ski? One falls over, or one doesn't fall over. It's as simple as that!' His friends would say later that he was the best skiers they knew.
Falling is a critical part of the learning process. It helps to reduce fear, and strangely enough often reduces injury if done properly! You must learn to relax; if you tense up as you fall you will hurt yourself far more. You normally fall when you go over your limit, and if you are developing a more positive attitude to skiing, this will happen often.
Accept that you are going to fall a lot and you will learn to relax while you are doing it.
Never despair because you are falling too much! There will be off days when you are always falling and can