Click connect in the graphic at the top of this page to open a telnet java client. That'll get you into the game but isn't the most desirable method. It's not the nicest view and backspace won't work so unless you're a perfect typist it's going to suck.
Whatever OS your on will probably have a telnet client built in. You need to connect to sindome.gigsville.org on port 5555.
The most desirable method and one you should seriously consider is to download a MU* client. These are basically telnet clients coded specifically for playing online games and have all kinds of cool features. Best to download a small one to start with then try other clients or look for peoples recommendations.
Once you have a client, again, connect to sindome.gigsville.org on port 5555.
Personally I recommend Gmud as a first client. Tiny download, simple and easy to use with a few basic useful features. That said, there's dozens of clients to choose from.
I say avoid Zmud, it's a huge DL, tons of features but probably way too complex for a first foray into MU* gaming.
Hopefully that should be enough to get you started.