The first lesson, of course, is that you cannot turn off human nature. You will have cliques, and you will gossip. Any activity in which milestones and competition figures centrally will generate strong emotion. Not everyone believes in the drama free rink.
But there are steps you can take.
Do your job
If you're a skater, show up for lessons. Follow rink rules, etiquette, and common sense. Take care of your stuff. Respect your coach and the others on the ice. If you're a coach, show up for lessons on time. Insist on proper work ethic and demeanor from your skaters. Respect other coaches' and skaters' space.
Be a grown up
No arguing in the lobby, or worse, on the ice. If you have a problem with someone take it OUTSIDE the rink. Maintain proper lines of authority--I don't care how hip you think you are, or how invested your coaching is in being the hip young coach. You are the coach not the buddy. This means a coach should NEVER talk about other coaches to students or parents.
Okay, okay, I know this is completely unrealistic, but try to follow the old Talmudic proscription, which I will amend here. Do not pass on speculative chatter about anyone. The ONLY gossip you should engage in is unassailable, confirmable facts. If you are in possession of an unassailable fact that could harm the subject but is not material to their position at the rink, do not pass it on. No one needs to know that the Skating Director's mother committed suicide, or that Coach A had an abortion, or that Coach B is on medication. Stop talking about the rink to the person who shared this information with you.
If you don't actually know the person being discussed, personally (like they know you well enough to remember your name), you shouldn't even be doing that, because really if you don't them, why do you care?
There are lots of other things to talk about--gardening, work, the price of gas.
Make yourself be nice.
Congratulate the skater who just landed an axel for the first time. Applaud all the skaters, not just your skater and her cohort. Make sure your skater does this too.
Don't interfere with, but don't be put off by, natural alliances
Kids, and moms, and gosh, coaches too I guess! develop their own friendships. Not all friendship groups are "cliques" in the destructive sense of the word. But a close-knit group is not an excuse either for them to disparage outsiders, or for outsiders to disparage and ignore them. Just because four moms (or skaters) are tight, doesn't mean you can't interact with them. Just because you have a tight knit group doesn't mean you get to be rude or dismissive of others at the rink.
Keep it in perspective
It's just skating. Even (especially?) at the elite levels. It isn't world peace, it isn't children starving in the ghetto.
How drama-free is your rink? What do you think helps keep it that way?