The software product designer interview is in multiple phases: online logic test, phone screening, design challenge interviews, and an on-site interview.
I got an email back after about 1 week asking me to take a logic and statistics test. The math test wasn't particularly hard, it was basic graph reading and statistics questions. The logic test was basically an IQ test with pattern recognition images. I felt like I did okay on both and then got a positive email back a few days later asking for a phone screening.
The phone screen was pretty standard behavioral questions, so if you are prepared for normal interviews this one shouldn't be very hard. They ask you some about your design experience and you have a discussion about the position and what you are looking for. Make sure you read about the company some before this interview.
After the phone screening, I was scheduled to do a 4 hour design challenge interview session the following week. The first thing was a presentation about the company and what they do. I thought this would be at the end, so I didn't ask many questions about the position because it didn't come up, but if you do want more details this is the time to ask.
The first design challenge was about adding a new feature to a current popular app. Make sure you are comfortable talking about design scope questions, considering user and business needs, and how you implement them. The second design challenge was about making two versions of the same app for two different companies. This one was similar to the last, but had a more technical aspect as well, talking about data retrieval and implementation.
The final design challenge was a data modelling exercise. You need to understand ERD or XML diagrams and be able to make one on the fly. This one was the most difficult design challenge, as it was only tangentially related to actual product design, and was mostly a database design challenge. My interviewer for this challenge gave me very little feedback and didn't understand or even forgot some of the questions I asked at the end of the session.
A few days after the design challenge interview, I got a rejection email. Apparently they have a company policy that says they cannot give feedback on the interview process. This is incredibly unfair to the interviewees, who spend 15+ hours preparing for the interviews and learning about the company. If the relationship is already not reciprocal to the workers, I am not sure how you would be treated working there.