Official Sochi tickets seller.
They released some tickets to people who'd expressed interests in the past. Randomly, of course. Had they offered me figure skating (non-dancing) events, I would have jumped. For people who get randomly selected to buy random tickets, the deadline is Feb 10.

Now, on Monday, Feb 11, at 12pm eastern, tickets will go on sale. So, plan accordingly.
I don't expect it to sell out like a Madonna concert, but popular events will go quick.