The basic objective of Go is to surround as many intersections on the board with your stones as possible. While this sounds simple, there are several additional rules that add great depth to the game. This is a great introduction on the rules of the game.
It's never been easier to play Go online! There are many Go servers out there these days, but as a beginner you can't go wrong with OGS. There are other options, however, these will require you to download a client in order to play against others. Both KGS and Tygem are two popular choices, as is Pandanet/IGS.
In order to measure the strength of Go players, a ranking system was created. The system divides players into ranks of Kyus and Dans. Kyus are typically students who are learning the game and as such correspond to a negative value. The lowest rank in Go is 30 Kyu which corresponds to a rank of -30. Dans are players who have acheived somewhat of a mastery of the game and correspond to positive values. The highest rank in Go is 9 Dan which corresponds to a rank of +9. More can be read here.
Don't worry! We've compiled a great list here for you to start getting better at the game. It's worth noting though that you probably won't see improvement right away. Like any other hobby, if you want to get good at Go you have to put a lot of time and effort into it.
Eidgo is one of the best online tools out there. You can learn joseki, mess around with positions, and even host SGF files of games you've played on it!
GoProblems is a site where you can practices tactics and sharpen your reading skills.
Reddit has an active Go community. Many of the members post interesting articles and will even help review your games if you ask nicely.
Go Kifu is a great tool to study and analyze professional level games.
Sensei's Library is probably one of the best resources on the internet. It has information and explanations on everything beginners (and even advanced players) need to learn.
The American Go Association is the head organization of Go in America. Determines player rankings in America, has listings of most Go Clubs and tournaments, lists news in the Go world, and has a useful resources page for links and equipment.