There are different ways to play Lands of Myst MUD.
LOM, as many other MUDs, uses telnet protocol. If you are a hard core player, simply
telnet playlom.com 4000
in your favorite terminal tool to connect.
LOM also has a basic MUD web client that allows you to connect instantly in your web browser. To play this way, simply open this link in your browser.
There are many MUD clients out there. They will allow you to play from a dedicated application on your desktop and allow for more advanced features like scripting and triggers. MUSHclient, tintin++ or Mudlet are probably a good starting point on desktop, MUDRammer for iOS and Blowtorch on Android.