I applied online. The process took 1 day. I interviewed at MIT (Boston, MA) in Oct 2019
Interview
Kind interviewer, we had a nice technical discussion. Then advanced questions on algorithms and data structures using a programming language like design a balanced tree, questions on complexity and programming exercises
Meeting with a professor, postdoc or professors are rather informal. Sometimes there are UROP postings online that give details about what the lab is looking for, but there is definitely merit to approaching professors personally or via email.
I applied through college or university. The process took 4 weeks. I interviewed at MIT (São Paulo, ) in Jan 2019
Interview
It involves the submission of 3 letters of reference. In my case, as I was overseas when applied, a Skype interview was set up. I know that if you are in the US, you are invited to come to MIT to deliver a 40 min lecture to the group.