I applied through university. The process took 2 months. I interviewed at SpaceX (Hawthorne, CA) in Nov 2012
Interview
Met people from Space X my college's career fair, talked with them about my experiences and gave them my resume. They liked that I had a lot of experience on real world projects and not just academics / school-related projects. Apparently they passed my resume around, and I later received and email invite to fill out an online application and a call to decide which department I would like to interview with.
I set up the phone interview and I talked with a manager a few days later. At first I wasn't sure how interview went, the manager was fairly monotone and unenthusiastic so that made it tough for me to sound enthusiastic, but we just talked about my experiences, what I wanted to do and he asked me if i thought I was qualified for some tasks (CAD, FE, etc.).
The next day (a sat.) I go an email from HR saying the manager I spoke to was very impressed and wanted me to fly-down for an on-site interview, all expenses paid (although I still have not gotten fully reimbursed 2 months later). Gave presentation on "a project I was proud of" for ~10min. The said they liked it a lot. Then they gave me an engineering exam (5-6 questions) which I was totally not expecting and probably cost me the job. Questions related to bending beam analysis, strength of materials, etc. (generally ME questions). Interview process was somewhat unorganized, just had me talk to random people who might be interested in taking me on for 5.5 hrs (talked to 6-7 people). Place seemed cool to be at but also extremely high stress, not a lot of smiles around the place.
Interview questions [1]
Question 1
Most difficult questions were on the written engineering exam (fairly short, 5-6 questions on forces on beams, strength of materials, etc.). Basic ME concepts that you learn in undergrad but I wasn't expecting to be asked those things and haven't seen it for awhile (been out o undergrad for 2 years so haven't reviewed the material lately).