You'll need a MU* client. Wikipedia has a page on them, or you can look on your search engine of choice. You may do better to search "MUD client".
Once you've got your client, point it towards tangent.dune.net port 8789. If there's not a separate field for the port, enter tangent.dune.net:8789. Once you get there, you can type connect Guest guest to log in as one of the guest characters.
A few basic things
Say - Also abbreviated as a single qoutation mark ("). Typing Say Hello, everypony! or "Hello, everypony! will have the same result - your character will speak whatever you've typed.
Pose - Also abbreviated as a colon (:). Typing Pose dances wildly or :dances wildly will have the same result - your character will perform the action indicated by whatever you've typed.
Movement - At the bottom of the description of an area will be a list of "Obvious Exits." Simply type the name of one of these to travel in that direction. Explore Ponyville and see who you can meet!There are several more in-depth guides available on the internet, but I've found that the in-game help files and experience are the best way to learn. Gammon.com.au has a good, albeit incomplete, guide. It covers most of the basics, but tapers off towards the more advanced topics.
Your Very Own Character!
Unfortunately, characters have to be added manually. Hopefully, this will eliminate or reduce players vying for recognition as the "real" Twilight Sparkle. Your understanding is appreciated.
If you want to play a canon character, mention it in your e-mail and explain why you think you'd be a good match for the character. If they are available, I'll let you know. If not, I'll try to find an acceptable solution for everyone.