Install a Distribution

You will need to install a LaTeX distribution. A good list is available on the LaTeX project website: www.latex-project.org/get/. If you use Linux, your package manager will surely have one.

An alternative is to use an online distribution, such as Overleaf. In addition to the online distribution, Overleaf provides a collaborative web-baed LaTeX editor. This is a pretty user-friendly and lightweight way to use LaTeX if you don't want to download any software and don't want to be bothered with technical details.

Choose an Editor

LaTeX files are text files which are then compiled to generate your document. You will need an editor to work on these files. Vim (my preference), emacs, and sublime text support LaTeX out-of-the-box, but also have plugins to integrate with your environment. There are also purpose-built LaTeX editors like TeXmaker and TeXnicCenter, so you should investigate which one you would prefer to use.

Getting Started

LaTeX is written in a typesetting language. You might download the .tex files of some homework solutions and use them as a template.

Overleaf also has some good tutorials.

Alternatives

Lyx is a graphical editor for LaTeX, somewhat similar to MS word. It will take some time to get the hang of it, but perhaps less time than learning LaTeX from scratch. I don't personally use this, but I know of 3 graduate students that used it to write their theses.

You could also use a combination of markdown and LaTeX. Kahn academy has a system called KaTeX that looks quite good. If you go this route, I recommend using your browser to print the html page as a pdf file.

The math typesetting of Libreoffice, Openoffice, and MS office is really not high-quality enough to even be considered as an alternative.