I had an atypical hiring process, in that it was extremely accelerated (1.5 weeks between the application and working my first day). There was a phone interview and two in person interviews, one with a Team Leader (manager) and one with a Group Leader (manager's manager) both in the same day. I was told after the second interview that I had the job and that I would be receiving a call (this is again not typical). Before the interviews, we had to watch a video and give comments - helps determine your personality type - and then take the typing/computer competency tests. I understand that the interview process has changed since then as you do the tests before in-person interviews.
Questions are very open-ended, again used to determine your personality as well as your problem-solving ability. They include "name a situation where your manager told you do something you didn't like" or "give an example of a time where you had a difficult problem to solve." I highly recommend using the STAR format, as the notes they take on your answer is in the format.
If you know someone who works at PayPal, USE THEM. It gives them a bonus and moves you to the top of the list. It also makes you a more likely candidate to get hired, as the hiring managers consider this a major plus. Even if you don't like the person, make sure they submit your resume for you after you apply online.