Note that this service is now known as overleaf.
I have to admit; I’m partisan. I think LaTeX is so much better than a word processor it isn’t funny. I avoid publishing in journals that won’t take a LaTeX document, I write minor documents and notes-to-self using it. I’ve even written fiction in LaTeX, for some reason that I can’t fathom. I mean, fiction is one thing that LaTeX is no good at. Manuscript format — double spaced, fixed-width font, underlines instead of italics — is practical but ugly. LaTeX is impractical but pretty… hang on, that’s not quite what I meant. What it does is lay your document out for you in a way that (mostly) conforms to the rules of good typesetting and page design.
These days, it is a whole ecosystem for handling anything from a bit of verse to a multivolume illustrated opus. But it can be daunting for a new user (I cordially dislike the term ‘newbie’). I’m not going to write an introduction to it, but I am going to point at writelatex.com as somewhere that is worth a visit.
It’s LaTeX for the cloudage. Runs in your browser. You can set up a URL and distribute it to collaborators or create a login and use it like googledocs (or whatever it’s called). It’s under intensive development at the moment, so it’s not finished, but if you’ve ever wondered what LaTeX is all about, but don’t feel like installing the bloated monster that is TeXLive (my only real criticism — does a LaTeX install really need to occupy all those GB?) then you can just go there and start monkeying around. If you really have no idea what you want to do, I would point you at http://www.tex.ac.uk/tex-archive/info/latex4wp/latex4wp.pdf (LaTeX for word processor users) and http://tobi.oetiker.ch/lshort/lshort.pdf (The Not So Short Introduction to LATEX2ε).
And then you can get started. Or not. Whatever.