In front of a live audience, Chris and Elecia talk about their experiences with FAA and FDA.
This show was recorded live in front of the Silicon Valley Automotive Open Source meetup group at Hacker Dojo.
The Wikipedia article on DO-178B is a good place to get an overview of the FAA process (even for other levels of concern).
For FDA, their guidance is the best place to start. Also see their 510k information. Finally, note that all class III (3, very high risk) require the more difficult Premarket Approval (PMA) process.
Everything we know about car safety certification, we learned by reading Wikipedia's ISO-26262, including Automotive Safety Integrity Level (ASIL).
Jack Ganssle's Embedded.fm episode was Being a Grownup Engineer.