LATEX is a widely used typesetting system in writing science (especially math) paper and books. It is a powerful tool and takes time to exploit its full features. Here we only give a very brief and “naive” introduction for typing homework assignments.)
You need to install two softwares (called packages in Linux): one is the back-end compiler and the other is the front-end editor.
Compiler: here are some common and free ones
Texlive: it has both windows version and linux version. For windows version, you can find the information about where to download and how to install it from here. Basically, you need to download the install-tl.zip, unpack it, and run install-tl.bat. You need to have Internet access when installing it. For Linux version, you need to install the package texlive-full. You can find it from Synaptic Package Manager in Ubuntu.
Mactex: it is only for Mac OS and can be found here.
Editor: there are quite a lot of choices, either free or commercial ones. You may find a list of comparisons from here.
You can choose whatever you like. I would suggest TexWorks/TeXShop/TexStudio for beginners. I am using Sublime Text (with LatexTools and LateXYZ), which contains more features and takes a little more time to learn.
A simple hint: If you installed Texlive from the above link, TexWorks should already be installed automatically.
Generally, you are only working with the editor and the complier will work automatically when you run from the editor. To make it simple to use, I created a template tex file. Please download it here and change it to whatever name you like. You can open the tex file with an editor such as TexWorks and make modifications according to the description in it. If you want to see the output, you can compile it with pdfLaTex or LaTex (click the green button in TexWorks). A separate pdf file with the same name will pop up and be saved in the same folder as the tex file.
You should be able to use it for homework now and you can always ask me for help when you have questions. If you want to learn more about LaTex, here is a very helpful website for beginners.
If you want to learn more about TexWorks, you can find a short manual from https://code.google.com/p/texworks/downloads/list
You may find a cheat sheet for some common LaTex commands from http://www.stdout.org/~winston/latex/
You do not need to install anything on your computer, but you need to have internet access to use it.