Every top-level national league in Europe recognized by UEFA gets at least its champion into the Champions League. The number of clubs a league gets depends on its ranking by UEFA. The top three leagues in UEFA get four clubs, the next three leagues get three clubs, the eight leagues after that get two and all the remaining leagues get one club.
Of all the leagues that get multiple clubs, all but the last qualifying club in each league immediately advances to the group stage. This means the top three leagues get three clubs into the group stage, the next three get two and the next eight get one. One final club--usually the champion from the highest-ranked remaining league--gets into the group stage. All remaining clubs must compete against each other for the remaining 10 spots in the group stage.
The top 15 clubs that did not automatically make the group phase (the lone club in each of the top 15 leagues) compete against each other in a two-round knockout tournament in the summer to determine five of the 10 remaining spots in the group phase. The other five are determined among the 38 or so clubs that remain. They take part in a similar four-round tournament. The draw for who, where and when each club plays is determined by UEFA.
The 32 clubs that make the group stage are paired into eight groups of four clubs. During the fall, each club plays every club in its group twice--once on its home field and once at the opponent's home. Standard soccer scoring rules apply, awarding three points for a win and one for a tie. The top two teams in each group at the end of the group stage move on to the knockout stage.
The 16 clubs that advanced out of the Group Stage begin a series of knockout rounds after a short winter break. At UEFA's discretion, each club faces a selected opponent in a two-game series (one game at each home field) with the club scoring the most total goals advancing. This knockout system continues until there are two clubs left. They face each other in a single game in May at a predetermined location to determine the Champions League winner.
Controversy arose regarding the draw rules after the 2005 championship. The English club Liverpool won the title, but its eligibility for the next tournament was questioned because it finished fifth in the English Premiership that same year. Despite no guarantee by the rules, Liverpool was allowed to compete in the next Champions League, giving England five clubs. The rules were altered after that, guaranteeing a defending champion a place in the next competition regardless of its domestic league finish.