Not being a competitive skiing athlete, being active in the martial arts and having been blessed with freakishly strong legs (until undiagnosed diabetes and injury did a number on me a couple of years ago), I never really had to train for skiing, but I've done lots of physio re-hab.
For what it's worth her are a few nuggets I've picked up over the years.
Pistol Squats - Don't load up your knees when they are bent past 90 degrees; just because you can doesn't mean you should.
Strength building - Do three sets, with between 30 seconds and a minute between sets.
Do not do heavy sets until you've been at it for a good six months. Once you're into the motion and are sure you're not going to injure yourself (if you are too stubborn you can injure yourself getting in that last rep), try to do it with the weight adjusted so that you can't quite get the last one in. Then after you're all finished your three sets of everything come back and finish off the ones you couldn't do. Adjust the weight, the time between sets, and the number of reps slightly so that last ones end up being a bitch to do. 5 to 8 Reps is heavy weight (sometimes 4
), 10 reps is normal weight. Eg. if doing 10 reps and starting out increase the reps (up to 12 to 15) before adding more weight and going back down to 10 reps. After a long time, when you can do heavy weights without hurting yourself, if doing 8 reps, put more weight on and do 5 reps when 8 reps is too easy.
Be careful.