When training for the sport of skiing you will want to develop strong quad muscles and cardiovascular endurance as these are going to be the prime determinants of how well you do at this sport.
One of the reasons you need strong quads for skiing is because you are constantly going to be in a bent-knee position so if your quads are fatiguing you are not going to be able to last as long and remain in the proper position.
Cardiovascular endurance is also essential for skiing because you will likely be going for a period of longer than a minute and a half and this is when your aerobic system begins to be called upon (up until that time the activity is primarily anaerobic in nature).
So to train for this you should practice doing an exercise called wall squats. This will not only build your quad strength but will also help muscular endurance as well so you are getting two benefits at once.
To do this exercise get a fitness ball and place it behind your back with the other side resting against a wall. Then slowly begin to bend at the knees and shift your weight downwards until you are in a sitting position. Hold this position for up to one minute and then stand up again to rest. Perform this exercise 3-4 times per session, 2-3 times a week and you will see significant improves in your ability to hold this proper skiing position.
Finally to work on your over all cardiovascular endurance try and either go for a few long runs a couple of times a week. Running is one of the best aerobic activities out there and will really get this system in shape quickly. Ensure you have a good pair of shoes beforehand though to make sure you do not suffer any knee or back pain.
Being sure to implement the proper exercises to train for this sport is one of the best ways to ensure you achieve maximum progress at it.