I applied through college or university. The process took 1 week. I interviewed at Tesla (Palo Alto, CA) in Mar 2015
Interview
First there will be a Phone Interview or may be two in some cases
You will asked mixed behavioral and technical stuff and mostly skimming your resume
Then you will have a techincal in-person or remote interview tasks.
They will soon let you know if you are selected or not
Interview questions [1]
Question 1
Questions will be mostly about your projects and about your programming skills