At startup, Emacs searches for a file called .emacs (or, on Windows systems, _emacs) in the user's home directory. This file contains Emacs Lisp code that is to be executed whenever Emacs starts.
In order to get Emacs to work with SML/NJ, you will need to create a .emacs file in your Unix home directory (you should start in this directory when you login to a Unix host).
At this point, you need to know how to load and edit files in Emacs:
C-x C-f is the keyboard shortcut for "find file" (equivalent to "open file" in a traditional office application). You will be prompted in the minibuffer for a filename; type .emacs to begin.
Emacs will open fresh buffer named .emacs. You should now add Emacs Lisp code to this file so that it can load the SML mode files; the exact changes are documented on the course web page's "Using SML/NJ" section).
Now, you want to save your changes. Hit C-x C-s to save the buffer to the file. If you wish to "kill" the current buffer, hit C-x k. This is roughly equivalent to "closing a file" in a traditional office application.
You need to restart Emacs, so that it can load the .emacs on startup. Hit C-x C-c to quit, then start up emacs from the command prompt.
Now, try opening a file called "first.sml". The modeline should say SML mode. You can now type SML code, and it will help you with indentation if you hit TAB: