Can I make a document, with a box to type stuff in, and when I press a button it refreshes, and saves what you typed(so next time i got to the document the box has what i typed before.

I am not entirely understanding in what situation.
First off, I don't think you are meaning a document on your working computer .
If it is an Internet Page there are varius ways to save it. If it is just temporary you can use Php Sessions; in case you want to save it for a longer time my guess would be a database, but if it is just few text files (few, not small) I think there are easier methods, but I don't know any of them.
Also, can you explain me the meaning of the title, thanks

Schimassek...

You would need a server-side application for that unless you want it saved into Javascript variable.

that goes to a more exciting world of website design or should i say website backend.

get to know php, after learning so, you may want to extend it to AJAX, which is pretty much javascript stuff but/and concentrates on parsing data quietly(no refereshing on the whole page).

dude, html evaluates your code on rendering your site, while your question goes to interactive website, which needs the aid of php yet there are more languages to choose from.