If you are not yet registered, go to http://tiddlyspace.com, and follow the instructions there.

This will give you a username and a password.

In addition you get a TiddlySpace of your own.

NB: You don't have to do anything with that space (wiki) at all if you don't want to (just leave it blank) - it is just a personal wiki that you could use if you want one. Some people use TiddlyWiki's as blogs, or personal websites, or - indeed - treatment manuals!

Once you are registered, you can:

(a) Open/create new spaces (see the User menu for instructions on how to do this, or go straight to Make a new space.)
(b) Make other people members of spaces (if you are a member yourself!)

Getting editing rights

If you want to be able to edit your team's local tiddlymanual, then you need to give your username (just your username, not your password!) to another person who is already a member of that space, who can add you as a member, using the Space menu for that manual. See Making someone a member of a space.