Stages:
If they believe you're a good fit, a recruiter will contact you after you submit your application/resume. (For me, they responded about a week after I was referred.) They will then schedule your interviews. There are 2 phone interviews, a Hangouts interview, and sometimes a third phone interview. (I was required to do a third phone interview; I suspect this might be because I did poorly on one of the previous phone interviews.) All interviews are technical and last 45 minutes. For the Hangouts interview, you might be asked a few short non-technical questions. After your interviews, they will contact you within about a week to tell you the hiring decision.
I can't give specifics due to the NDA, but they asked questions about data structures and algorithms, similar to what you might find at any other tech company.
The following metrics were computed from 11 interview experiences for the Google Engineering Resident role in United States.
Google's interview process for their Engineering Resident roles in the United States is fairly selective, failing a large portion of engineers who go through it.
Candidates reported having very good feelings for Google's Engineering Resident interview process in United States.