Tournaments are some combination of three phases – qualifying, group stage, and knockout round.
In most club cups, the qualifying round is the previous year’s season (somewhat similar to the seeding system for NCAA’s March Madness). For example, the top three finishers in the 2008-2009 England’s Barclay’s Premier League were guaranteed a spot in the 2009-2010 Champions League tournament. Qualifying for an international cup is normally determined by a prior tournament, i.e. you win tournament X and get into tournament Y.
The group stage is round-robin (you play everyone in your group once or, depending on the cup, twice). A win in the group stage awards 3 points. A tie grants both teams 1 point, and a loss is worth no points. The two teams with the most points advance to the knockout stage.
The knockout round (also referred to as knockout stage) consists of the teams that advanced out of their groups. It can be a single-elimination round or a two-leg tie (one home game/one away game). Determining the team that should advance in a two-leg tie can be quite complicated:
A team that wins both games automatically advances. In all other situations (both teams win a game, both games are ties, one teams wins a game and the other is a tied), the team that scored the most goals advances. However, if the total number of goals scored by both teams is the same, the side with the most away goals moves on. And if the total number of goals are equal and the amount of away goals is the same, then the last tie advances to extra time. After extra time, if the teams are still tied, the game is finally decided by a penalty shootout.The total number of goals scored over the course of the two games is referred to as the aggregate score.