In preparation for competitions the skater must improve their anaerobic endurance, since the skater's heart rate is way above what they could maintain for any length of time. For the rest of us, aerobics classes are a good bet. Find one with lots of floor work and stretching. Stair climbing is excellent. Try taking them two at a time.
Weight training is also good, especially for improving jumps.
But weight training is not for kids because of the potential for long term damage of a growing skeleto- muscular system. In skill sports, such as skating, there are two schools of thought here. This supposedly will prevent psychological and neuromuscular confusion over whether you're performing the desired skill, or the weight activity that's like it. The first school would appear to be appropriate for relatively static skills like a sit-spin. This is because an activity that is similar to this activity is going to have the broadest effect upon all the muscle groups involved in the activity, rather than just isolating certain muscles.