There are lots of places to play go on the internet. The most popular one is probably
IGS, the Internet Go Server. It has hundreds of people on at all times, and many strong players. Sometimes pros come on and play amateurs, and sometimes mysterious people come on who win almost every game - there is a theory that they are top pros out having fun. Also, sometimes it broadcasts pro games. The problem with IGS is that it is run by an
authoritarian named
tweet. He regularly greps the chat logs and bans anyone who mentions any other server. He also bans people if he finds out they are even associated with any other go server. IGS also checks your IP address and won't let you login if you are in
Japan unless you pay.
There are other go servers: KGS, LGS, NNGS, and some abandoned ones. They are smaller, but friendlier. They don't have as many extremely high ranked players on them, but they have quite a few pretty good players, and people are much nicer there.
There are many go clients, I prefer jago, but I have also used panda-egg.
In general, playing go on the internet is like playing chess on the internet: it's more abstract than playing in person, and it's harder to concentrate through a whole game. However, since it's hard to find good go players in real life, playing go on the internet is great.
Playing go online has one advantage over chess, in that there are no good computer go programs. So you don't have to worry about someone using a program against you. There are some joseki (opening) libraries, but there are many ways to move out of standard openings that don't give you too much of a disadvantage. There are non standard opening moves that are probably only a tiny bit worse than best play, but which pros never play and so therefore won't be in opening libraries. Since the variation in amateur games is so high, playing one won't automatically lose the game for you but it will force a cheating opponent to play honestly.