Open up emacs.
Press C-x C-b. (opens up list of buffers)
Click *scratch*.
While the cursor is in the bottom screen, hit C-x 1 (this is just to make it easier to read).
Delete the text in between the semicolons (which should be all of it).
Type what you want to (for example, (+ 2 2)).
Press C-x C-e. (this evaluates the list)
Your result (in this case, 4) will be displayed in the minibuffer (the small line at the bottom).
NOTE: This is just for small statements such as (+ 2 2), I'm guesing, because I'm a newb as well.
Also, a good guide to elisp (Emacs Lisp) is
Programming in Emacs Lisp
Hope I helped.