Submit CV to all potential PI, Some may reply and ask more detail about your bg. If they find a good match, they will either make a skype call or invite you to meet on site (in their office). The meetings are quite different depending on profs. Most people will ask some general questions in their field and ask what your interests are.
Was asked some technical questions and general experience. Everything done through Skype. Interviewer is my future direct supervisor, is very knowledgeable and kind. Questions asked are relevant to the job.
I applied online. The process took 3 months. I interviewed at MIT (Cambridge, MA)
Interview
The process from online application to initial phone screen took almost 2 months. Recruiter on phone interview did not give a background or greetings, just jumped right into a bunch of (about 10)tough behavioral questions that has nothing to do with the actual job responsibilities. Felt like I was being interrogated. Zero interaction, no feedback or anything before jumping to the next questions. It was obvious that questions are from a list and recruiter was reading one after another without really paying attention to my answers. Overall was a very dull and unprofessional phone interview.