I applied online after being referred by a SpaceX employee, and within a week a recruiter called for screening. He asked questions about my resume, knowledge of SpaceX, and went into detail about the position. The recruiter then set up a phone interview with the manager and lead engineer of the team. The phone interviews were done separately, and basically just went more in-depth with my knowledge of manufacturing processes, achievements, and how I could apply that at SpaceX. Shortly after, I was scheduled for an on-site interview.
Once arriving on-site, I was given a brief tour of their incredible facility. My recruiter wasn't able to answer most of my questions, so the tour was definitely not great. I was then set up in a room to give a technical presentation on the most challenging project that I drove to success. The presentation panel consisted of around 10-12 engineers, managers, and production supervisors. After the presentation, the panel met privately and decided that they wanted to move forward with the one-on-one interviews. The first one-on-one was a lunch interview, which can be a bit difficult/awkward, but the attitude was casual and it went very smoothly. The next 5 or 6 interviews were with a variety of engineers and managers who were all incredibly smart, friendly, and passionate. There were very few if any trick questions... they weren't trying to stump me or see if I was a genius, just making sure I was qualified and a good fit with the team (the way an interview should be).
I left the interview with a very positive impression, and then the wait began... It took about 4 weeks after the interview before I received an official offer. I believe the majority of the delay was the fault of my first recruiter, who really dragged his feet for a lot of the process. In the middle of the process, he left the company (not sure if he quit or was fired) and I was assigned a new recruiter. From there on out, everything moved much faster. I was asked to re-submit my list of accomplishments, which was reviewed/accepted by SpaceX executives, and then I was offered the job!
Overall a great experience. The process was long and difficult at times, but well worth it for a shot at working for such a revolutionary company.