After to responding to an ad online about the job, I received an email from the PI offering me an interview. A week later, I had the interview with the PI and met some of the lab members. Two days later, I received a call from HR asking me to come in for an HR interview since the PI was strongly considering me. The HR interview was with a Talent Acquisition Specialist. While there, I had to fill out an application and list my work history, as well as supply a copy of my CV.
The HR interview was fairly standard, no curve ball questions. Mainly why MSKCC, explain why you're leaving your current job, greatest accomplishment, future goals, how do your skills match the position, etc. She also explained the benefits during this time.
About 3 days after the HR interview, I received a call from the specialist and was told that the PI wanted to offer me the job. I gladly accepted and was then informed that I would be hearing from someone else in HR to assist with the Onboarding process. This includes a mandatory urine drug test, background check, physical exam (exam + 2 TB tests), and filling out of tax forms and other HR paperwork. Be aware that an outside agency does the background check; this is not the same as checking references. They simply will confirm that you worked everywhere you list that you have worked the past 7 years and verify your education credentials. They are very thorough! They couldn't confirm one of my past employers over the phone with the company so I had to fax them my W2 proving I had worked there. Be sure to provide as much information as possible for the background check to avoid delays.
Overall, the hiring process took about 3-4 weeks to take care of all pre-employment clearances and paper work. Once you're all set you'll attend new employee orientation for two days, then your first real day of work will be that Wednesday.