How to configure Xdebug in PhpStorm through Vagrant

This guide will explain how to configure PhpStorm to use PHP's Xdebug extension through Vagrant. The process is not as straightforward as it should be, and available documentation has not been clear on this usage. It will be significantly easier when PhpStorm 8 is released, due to its ability to define remote interpreters. When that is available, a new post will be written, with a link to it from this one.

Update Feb. 22, 2015: PhpStorm 8 was released late 2014. As indicated in the original publication, the steps to take advantage of remote interpreters will be delineated. The process