LaTeX
Please scroll through the entire page--there's a lot of info/goodies here.
How to get LaTeX:
For Mac users: try MacTeX.
For Windows users: you're basically going to use a version of MiKTeX.
For those who do not want to download anything ever:
ScribTeX. All you need is an email address. It's very bare bones and has an automatic compiler, etc.
writeLaTeX. Again, all you need is an email address. You can pay for "extras" on this site (like Dropbox syncing, etc.); however, it does provide free templates.
Don't worry about downloading in general, though--as xkcd will tell you, .tex is "safe".
How to find a particular symbol:
Detexify. Coolest thing ever. There's also a phone app--which is free. Great if you only want one symbol and/or have great handwriting.
"The Comprehensive LaTeX Symbols List". This is what we had to use in the dark ages before Detexify.
Other resources:
LaTeX Stack Exchange. It's an open forum for questions, usually regarding compiling issues and atypical formatting styles.
Handouts on LaTeX (made by me, for MAT230 students):