Currently (2013-04-01) the list of Leagues is:
- Bronze League: 8% of all players
- Silver League: 20% of all players
- Gold League: 32% of all players
- Platinum League: 20% of all players
- Diamond League: 18% of all players.
- Master League: The best 2% of all players. It is impossible to qualify directly into this League.
- Grand Master: The top 200 players in a region. Is created only after 2 weeks into a new season. Players that are not active for a certain time get demoted to Master.
Before you are placed in a League, you must play 5 Placement Matches against random opponents. After that, the game tracks your skill by assigning you a matchmaking rating (MMR), which is not exactly your League points, but similar. Different Leagues correspond to different MMR ranges, and it is possible to be promoted or demoted, if your MMR stabilizes within another League's range.
After a Season ends, all Leagues are wiped, but MMR does not. To be placed in a new Season, you have to play one Placement Match, which does not actually mean more than any other match - it is just there to filter inactive players from League rankings. Skipping several Seasons does reset your MMR.
Since some patch there is also a button to Leave League - if you feel that your MMR is well in another League (like if you are constantly encountering equal opponents from there), but a promotion just doesn't come, you can try to force it. Note that this doesn't reset your MMR, of course.
There is also a special, Practice League. When you start playing on a new account, you are placed here, and can play fifty games here before your placement matches into "real" Leagues (you can leave whenever you want though). Practive League matches are played on a special, more "noob-friendly" maps, that have destructible obstacles completely blocking bases off, eliminating early pressure. After you leave Practice League, there is no way back ever.
Further reading: Starcraft Wikia