Basics of drafting:
The players (6-11) sit around a table and are given three booster packs. They open one, take a card from it, and pass the other cards to the player on their left. Then they take a card from the pile they were passed and pass the remaining cards to the left. This continues until all the cards have been picked. The process starts over again for the second and third packs, with the players passing right for the second pack and left again for the third. After all of this has been done, players each make 40 card decks using the cards they drafted and basic lands that are provided by the tournament organizers. Then, everyone plays in a tournament with the decks they made. Afterwards, everyone gets to keep all the cards they drafted.
Drafting is a popular format that should be available at pretty much any store that holds regular mtg tournaments. Entrance fees are typically around $15, which is pretty decent considering that you get three booster packs worth of product just for playing. Drafting is a particularly good format for people who don't want to spend the time or money required for standard, but still like to play regularly.
I know all of this pretty well because at Purdue, I organize drafts every week. (Next semester, I'm planning to time them around ssbo's better so I can come more)
As for magic in China, there were a couple of shops that held tournaments. Not as popular as it is in the US, but I still didn't have a problem playing every week. They had this other Chinese game that seemed similar to magic that I saw people playing all the time, though.