You have to be 17 or older at the Junior/Senior level.
Disney on Ice is staffed by Feld Entertainment. Feld's recruiting requirements are on their website.
Feld Entertainment also staffs other skating shows for cruise lines and amusement parks, so there are other opportunities beyond Disney on Ice.
They do not require any particular freestyle elements, such as triples. They're looking for on-ice actors with good core skating skills (spins, edging, spirals, etc.) You start by sending your resume to the company. If they're interested, they'll arrange an audition. I've seen some on YouTube and others have sent videos by email/DVD. In a few rare cases, they'll do a live audition while they're on tour in the skater's area, but that doesn't happen very frequently.
There's a lot of competition for the slots, so you do have to be extremely good at skating overall. If you have a particular odd skill, such as juggling or acrobatics on ice, that's a benefit.
There's a professional organization called the "Professional Skaters Cooperative," aka http://www.proskaters.org
that posts up-to-date information about show opportunities and tryouts. Worth checking out if you're serious about becoming a show skater.
That's a really hard lifestyle - while you get to travel, you don't always have time to see much other than the bus or airport and arena, the pay is sort of low and you have to pay for your own expenses from it, not to mention sharing rooms and dealing with weigh-ins.