A Googler posted on their blog that they were looking, so I emailed him and he referred me. At the time I had dropped out of an EE+CS degree, had four years of suit-wearing professional experience writing enterprise webapps in PHP and ColdFusion, was halfway through a part-time Masters Degree in Design, and had a bunch of small JavaScript/C++/Art side projects. They hired me as a SWE, am now in UX.

I won't pretend that I wasn't very lucky in timing, interviewers, etc, but you won't get anywhere if you don't roll the dice.