I applied in-person. The process took 1 week. I interviewed at Yale University
Interview
Simply contact a professor and say you want to work for them. They will usually just have you come into their office and tell you a project that you can work on -- may not respond or just say no if they don't have anything for you to do in their lab.
Interview questions [1]
Question 1
What are your interests, why do you want to work on X project