I met a recruiter at my school's career fair. I apparently impressed him, because I received an invitation to apply. SpaceX looks at your resume for all positions, so the position I applied for was not the one I was considered for.
About a month after the career fair, I was requested to interview for a position as a propulsion design engineer, which was one of the fields for which I expressed interest during the career fair. I was contacted by a member of HR who asked me a couple quick questions. One of them was to confirm that my GPA was the one I stated on my resume, which was a strange question in my opinion - I listed a middling GPA. Afterwards, we set up a time for a group phone technical interview. Details were sent to me by email.
The interviewers were three members of the propulsion design team - two senior engineers and one junior engineer. They took turns asking me questions about my knowledge and experience, and also asked me a couple things about GD&T, phrased in a way I wasn't expecting. My program doesn't teach GD&T so I fumbled the question rather badly. A couple weeks later, I was contacted by phone and informed that I was not selected for further interviews.
The experience was a good one. SpaceX was very professional at all levels of the hiring process.