Teams (not players) assemble into random drafting circles (called pods) of roughly equal size at the direction of the Head Judge. Teammates sit next to each other. Tournament officials then distribute identical booster packs to each team in the pod.
After opening and counting the cards in their first pack, the team chooses two cards from the booster pack then passes the remaining cards face down to the team on its left. Selected cards may be placed into one or two piles. The cards chosen are not assigned to a particular player; they become part of a pool out of which both players will build their decks. The open packs are passed around the drafting pod—with each team taking two cards from each before passing—until all cards are drafted.
For the second pack, the direction of drafting is reversed as usual. Thus, the overall draft direction is left–right–left–right–left–right.
Also remember that while drafting is typically a time without discussion, Two-Headed Giant is absolutely an exception. Players are allowed to communicate with their teammates and assist each other (as they are making picks together, as a team).