Here's how it works: A beer cooler is designed to keep things cool. It accomplishes this with a two-walled plastic chamber with an air space in between. This airspace acts as an insulator, preventing thermal energy (a.k.a. heat) from outside to reach the cold food inside. Of course, insulators work both ways.
Once you realize that a beer cooler is just as good at keeping hot things hot as it is at keeping cold things cold, then the rest is easy: Fill up your beer cooler with water just a couple degrees higher than the temperature you'd like to cook your food at (to account for temperature loss when you add cold food to it), seal your food in a plastic Ziplock bag*, drop it in, and close your beer cooler until your food is cooked. It's as simple as that.
-- Serious Eats: Beer Cooler Sous Vide