Same as original Flip Cup, just with a different way of determining a winner. 
You usually need at least 6 (but up to 12) players, each with a cup 1/4 to 1/2 full of their beverage of choice. The teams are divided equally and placed directly across from each other on a long table (3 on one side, 3 on the other). The teams decide which end of the table starts first and how you want to begin. (Counting to three, reciting a certain quote, etc) After the first person chugs their beverage, they place the cup right side up on the edge of the table and flip it until it lands upside down. As soon as the first cup lands upside down, the second person on that side of the table can chug their beverage and begin to flip. It’s a race from one end of the table to the other. Whichever side loses, must vote off one member of their team, but the number of cups must remain the same. (If you started with three people on each team and your team is down to two people, someone must drink two cups). This is continued until a team is down to one person and loses. If a tie occurs (last cups land upside down at the same time- believe me, it happens), these two people must face-off. Their cups are filled to the top with their beverage, chugged, and then begin to flip. Whoever loses this face-off is automatically the one voted off their team.
(Thanks Kym!)