LaTeX is the standard document preparation system for mathematics.
Overleaf guide (web-based editor that is convenient for collarborations)
MiKTeX manual (TeX distribution for Windows, Linux, and MacOS)
MacTeX FAQ (TeX distribution for MacOS)
The easiest way to get started is to use the all-in-one online editor/compiler Overleaf. No downloads necessary. It is particularly useful for collaborative projects.
For local installation on Windows, pair the MiKTeX distribution with your TeX editor of choice, which requires a separate download. I have had good experiences with TeXStudio and TeXnicCenter.
For local installation on Mac, install MacTeX, which comes bundled with the editor TeXShop.
Once your TeX editor is properly configured (see official guides below), it is time to create a new .tex document and start writing. The first few lines of your .tex document consist of code that tells the TeX compiler how to perform its job. A minimal example might look as follows.
\documentclass[12pt,letterpaper,reqno]{article}
\usepackage{amsmath,amsthm,amssymb}
Line 1, \documentclass[OPTIONS]{CLASS}, dictates the overall appearance of the compiled document. Some common document classes include article and amsart. The three optional OPTIONS used above forces a 12-point font size, letter paper size, and right-aligned equation numbers.
Line 2, \usepackage{PACKAGE}, loads various tools that adds functionality. Above, three canonical packages from the American Math Society are loaded. Other useful packages include fancyhdr (creates headers and footers), geometry (enables detailed customization of page layout), hyperref (automatically generates hyperlinks for cross-references), and mathtools (enables many advanced functionality features).
These lines of code, which take place before the document-proper, make up the preamble of a .tex document.
Once compiled, all content sandwiched between \begin{document} and \end{document} is visible to the reader. Text can be typed out as-is. In-line mathematics need to be enclosed by $ (dollar signs). Display mathematics need to be enclosed by \begin{equation} and \end{equation}. Below is a minimal working example.
\documentclass[12pt,letterpaper,reqno]{article}
\usepackage{amsmath,amsthm,amssymb}
\begin{document}
Let $x, y \in \mathbf{R}$. Assume $x < y$, then we have
\begin{equation}
y - x > 0.
\end{equation}
\end{document}
Click here to view the resulting .pdf output.
Overleaf's LaTeX in 30 minutes and LaTeX documentation
Short Math Guide for LaTeX by the AMS
The Comprehensive LaTeX Symbol List maintained by Scott Pakin