I applied directly through SpaceX.com. I was first contacted by a recruiter and some days later by a QA Lead, these conversations were not very technical.
I was then scheduled for an in person interview to which I was offered to be flown in and hotel accommodations provided. I opted to rather make the commute by car and was provided accommodations. I was asked to do a write-up addresses to the CEO stating Academic Achievements, Top Accomplishments, Career Transitions explanation.
The interview consisted of meeting 2 Software Engineers, a QA Engineer, a Business Analyst along with Department Director. The Software Engineers asked me to identify syntax errors in a short piece of code and 2 other very basic technical questions. The QA Engineer made the interview fun and interesting, the questions were tailored to understand my thought process as opposed to technical questions. The interview with the Business Analyst and Director was lengthier and involved the typical questions of why I'm changing jobs, what my weaknesses are, etc.