Starting with you, each player separates all permanents they control into three piles. Then each player chooses one of their piles at random and sacrifices those permanents. (Piles can be empty.)
2/1/2014 To choose a pile at random, each pile must have an equal chance of being chosen. There are many ways to do this, including assigning each pile a number and rolling a die.
2/1/2014 You may put Auras or Equipment into one pile and the creatures they were attached to into a different pile.
2/1/2014 If you put all permanents you control into one pile, you’ll have a two-thirds chance of not having to sacrifice any permanents, but a one-third chance of having to sacrifice all of them.