Effie Trinket is the District 12 escort and the person in charge of naming the tributes for each annual Hunger Games. If you're playing that drinking game, you may also want to chug your beverage when she says her signature line, "May the odds be ever in your favor!"
Cinna is Katniss' stylist and the man who makes her the "girl on fire." You'll know when you're supposed to drink for Cinna.
Haymitch is a former district 12 victor, and current advisor to Katniss and Peeta. He's also a drunk. You should probably take a drink every time he takes a drink.