sit ups pull ups

Any skater who is serious enough to retain a coach to train for competitions quickly recognizes the importance of off-ice training.  Besides ballet, USFSA also recommends strength training; see their general guidelines for strength training here.

Boring as heck, three strength exercises are essential to getting to the next level: sit ups, pull ups, and shoulder presses. Sit ups provide the strength to keep a straight core and properly aligned spine while you spin. Shoulder presses allow you to maintain control over your arm movements.

Everyone though seems to overlook pull ups. The back muscles strengthened by pull ups do more for your posture than any other muscle group.

Once you move up to elite you likely need a more serious and educated personal trainer.  See  for example this article by Charles Poliquin of how he has trained world-class Canadian skaters.

Some basic strength training at the rink or at the gym is infinitely helpful to your competitive skating, but once you get committed at a national level be sure to kick your off-ice training up to the next level.

- freestyle

When you are a young kid starting to skate you begin with classes at your local rink. Then once you've got your balance and a slow scratch spin (and decide that you'd like to try something more serious) you get the idea that perhaps you can get a coach. Then after you've had some coaching at public sessions for around a year, and you've got a couple spins and a simple jump or two, your coach will want you to attend some freestyles.

Away from the classroom setting, the freestyle is where you really get your eyes opened to what skating is all about. Most freestyles have a few up to around a dozen skaters. Here you get to pay detailed attention to how the other skaters "carry themselves" and present their showmanship.

Once you reach the stage of skating freestyles regularly, it's an excellent idea to attend freestyle sessions at nearby rinks (other than your own home rink) even if you go it alone without your coach. Rinks vary so much in the culture and style of their skaters that you will gain a broader sense of methods and embellishments by traveling around and observing.

Yes it can be a little intimidating to walk into a new rink to spend an hour on the ice with gals you've never seen before. But at heart they aren't that much different from you; be assured that the sisterhood of skaters have way more in common amongst themselves than differences. Go, introduce yourself, relax, make new friends, and expand your horizons. The benefits are well worth the wee bit of initial embarrassment.