Directions. Located inside a youth hostel which is very close to the west entrace (on east side of the road) of a Lishi hutong (礼士胡同) about 200 m south of Dongsi subway station (Subway line 5). The hostel has a big sign that says 161客栈. It's a nice place, very cheap for beijing, with couches and coffe tables around, and it's not very smoky either! The owner is nice, so just come in and look for us.
Subway: Line 5, Dongsi station, exit C and head south. There will be a sign for lishi hutong in front of you. Turn left there and go about 20m- the hostel 161 will be on the left, across from a hotpot place. We meet inside on the little balcony thing on the 2nd floor.
This is a great way to learn the rules and the basic idea, without anybody looking over your shoulder. When you start, just click around til you figure out what's going on. It'll start you with a big advantage. Once the computer passes, click "pass" yourself and it'll score the game. If you keep winning, it'll give you less and less of an advantage.
You can also check out Go Child, a really fun site with lots of problems from absolute total beginner level up to higher levels. It's designed to make the game interesting for kids, and it achieves its purpose well.
If you have been playing for a while, and want to seriously get better, I recommend goproblems.com. Make an account and try the time trials, or just go through the problems. After logging in, click 'problem', 'all unsolved', and with a difficulty of 'at least 25k'. You should be able to blaze through these at first, but keep going. As you have solved more and more, remaining problems will get harder and harder until you find your level. Most problems here have variations showing the continuations, too, which is good for complex problems. You can also add comments with variations you think are wrong or missing. This site can get you all the way from 'just learned the rules' up to very high amateur level. The more effort you put in here, the more you will get back over the board. An interesting thing about people studying to be pro is that they spend more time doing problems, especially life and death problems, than they spend actually playing games.
A cool site for go news is go sensations. It's got game reviews of selected games from the big go servers. It's run by the same guy who made the insei league, which is a league for studying go, which has groups playing on KGS & dragon. And there is also baduk.pro, which is a social network for go players.
Also, here is a local copy of the modified cgoban client called cgoban-h, which has a number of improvements over the official version. (this is a new version, which works with KSG 3.5 (updated january 2012)). This is included here as a demonstration of the great usability improvements possible in the KGS client; however, it's not officially approved by the KGS apparatchiks. To try the features, right-click and do 'save as' - then, run the file and connect to kgs in the normal way. (on linux, java -jar cgoban-h.jar, once you have java in your path ("which java" has to succeed))