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
To move to a higher league, you have to simply play well, win matches and rank high in your league. Then you might be promoted to a higher league. Same goes with demoting - play bad, get to the bottom of the ladder and you will be demoted to a lower league.
When playing matches, you might encounter players from almost any league i think. I personaly am ranked in a platinum league and played a few matches with gold or silver ranked players. You will see that sometimes the load screen reads "Slightly favored" or "Favored" above you or the oponent. That means one of you is considered better and the game thinks he/you should win.
Best Answer
I don't know what it is by design but I can provide statistics on a per region basis. Bare in mind, this is where players are, not where they belong (so they maybe better or worse than they appear).
These numbers would seem to suggest the following:
Update:
At Blizzcon 2010 Blizzard announced that they would add two new leagues with the following requirements: