It's mostly guesswork right now, but I'd put my money on a system similar to the auctions. Contests probably for the most part will be composed of a theme to design your Savii for, along with a deadline date, and a set prize. The contest menu would show ongoing contests in one area, and finished contests containing results in another. Ongoing contests would allow selection from one's Savii album, maybe also showing the number of entries. Saviimins would be the only ones able to create new contests. Prizes might include things like points, bucks, extra slots, limited edition Saviis. Again, this is all just speculation.
According to SavantInamorata, they'd be a once-a-week thing, in addition to larger contests with expectedly heftier prizes occurring less often (guessing that means on a monthly or holiday basis). Entries can be submitted and voted upon (by anyone) within 3 days of the contest's start, and winners announced at the end of the week.
Saviis, not to mention the future contests, have been put on hold for a long time, so even such information isn't entirely reliable. We'll just have to wait and see.