I had an initial phone screen with a product manager from another group. Then I had a series of face to face interviews with other product managers and with an engineering manager. These interviews consisted of real-world Google product manager problems and discussion of how I might attempt to understand those problems and resolve them. A few weeks later I met with a manager and was asked similar questions about problem solving and another question about a product that I like to use, why I like to use it, and how I would improve it (other interviewers had asked this one too). Finally, again a few weeks later, I met with a Director and the process was repeated. After the interviews were finished, the information was sent to a hiring committee and my candidacy was voted on.

You would have to do a hiring assessment first, then a recruiter screening follows. First round interview with the hiring manager. Majorly product sense and product improvement. The questions were not direct though.