The SitePoint PHP blog has a new post from Matthew Setter today sharing a Composer cheatsheet he recently discovered with an example of the common commands and "composer.json" file structure.
Unless you’ve been living under a rock, today’s PHP isn’t your grandmother’s PHP; it’s an entirely different, much more elegant and mature language with countless improvements and additions. One of the key additions is Composer, the de facto standard for managing PHP project dependencies which, by default, gives you access to hundreds of ready-made libraries, via Packagist.org.
He goes through the parts of the guide, introducing some of the commands and covering the details of the full "composer.json" JSON structure. There's also a video introduction if you'd like the more visual version.