This is one of the most popular/common games played in golf. It is typically seen in Charity Events, Golf Association Events and other types of tournaments. The most common teams for a Scramble are 2-person or 4-person teams. In a 2 person scramble, sometimes USGA handicaps will be necessary and implemented, but in most 4-person scramble tournaments, handicaps are not used.
This video, featuring PGA Professional Todd Kolb, shows how the Scramble Format is played. It is described in the 2-person format.
All players on the team will tee off. After the tee shots, the most desirable shot is then selected and all players from the team will hit the next shot from that location. After the 2nd shots are played, the best shot is selected and so on and forth. This system is followed, selecting the best shots from each location, until the ball is holed out.
For info on the match play format, click here.