Software for LaTeX

To use Latex, you will need both a compiler and editor. The major compilers are: Any editor that can edit plain text files is capable of editex .tex files. The following editors provide nice features e.g. syntax highlighting and easy compiling Some choices for editor A long discussion of the properties of various editors can be found at the StackExchange.
Personally, I use vim to edit tex documents, and TexLive to compile them.

If you're using a Mac, I highly recommend getting MacPorts. This will (among other things) allow for an easy installation of TexLive.

Resources for learning LaTeX

For writing up homework, here is a template you can use to get started.

If you like to learn by example, here are some homework assignments I tex'ed up a few years ago. The Game Theory examples require the pgf/tikz library to compile. Depending on the latex compiler you are using, you may have to install this separately. It's a great library though, here's a nice user guide (pdf) for it.

latex examples

Source Compiled

Probabilistic Method HW1
Probabilistic Method HW2
Game Theory HW7
Game Theory HW8

Probabilistic Method HW1 (pdf)
Probabilistic Method HW2 (pdf)
Game Theory HW 7 (pdf)
Game Theory HW 8 (pdf)