All four players play their own ball throughout; at the end of each hole, the low score between the two partners on each team is that team's score. For example, Players A and B form one team. On the first hole, A scores a 5, B scores a 6, so the team score is 5.
Four Ball can be played as stroke play or match play and is one of the formats used at the Ryder Cup.
Handicap allowances for various Four Ball competitions can be found in the USGA Handicap Manual, Section 9-4 (www.usga.com).