Captains comes in two varieties, five man Captains or four man Captains. A very similar 3 man game is called Wolf.
At the start of each hole the captain chooses another player as his partner. The Captain and his chosen partner play low net, low total against the other players. In 5 man Captains the team who was not chosen by the captain use the best two scores from their three-some against the Captain and his partner.
Immediately after the captain tees off he may choose to "Go alone" for double points. He then plays his score against the other three players. By the same token once the captain chooses his partner, he may deny the captain and "Go alone" for double points.
The Captain on the first hole is selected by tossing up a tee. The rest of the tee order is also established in the same manner. The tee order is rotated and followed throughout the round. The first person to tee off is the Captain.
Wolf: When playing Captains with Wolf rules the captain must pick his partner immediately after a player tees off. If he picks no one, he's stuck with last player to tee off. This rule is common in 4 man captains but can be used in 5man Captains as well.