I applied online. The process took 5 weeks. I interviewed at SpaceX (Hawthorne, CA) in May 2015
Interview
Brief non-technical phone screening interview followed by technical assessment test followed by technical phone interview followed by onsite interview. Onsite interview consisted of giving a presentation of a previous project followed by Q&A, getting a short period to study a field study case and then present your results and analysis of that, given a tour our Hawthorne facility, given a small written exam with technical engineering questions, and then a series of several one-on-one interviews with different members of the team. The on-site interview was supposed to take 4 or 5 hours, but ended up lasting about 7 hours. Very positive and educational experience.
Interview questions [1]
Question 1
You have an inflated balloon held shut and then suddenly let goof the opening, plot the diameter of the balloon vs time, and explain your assumptions.