For the most part they are text-based, although some also have HTML or graphical aspects. Or Multi-User Dimension. Or Mauve Ugly Ducks. In the simplest case, you need a telnet program. You probably already have one on your computer.
Most MUDders use what is known as a client program.
This is a program designed as an interface to a MUD, so it has MUD-specific features that a plain telnet program lacks. These features often include allowing multiple sessions at once, color-coding text, and creating macros to simplify the entering of MUD commands. MUDs have found many different uses. In education, they may be used as virtual classrooms or as simulations of some setting being studied.