First, I had to fill out an online coding test at HackerRank. It was pretty simple -- I had 3 hours to do two basic programming questions. Then, there was a phone interview; I was asked to expand on certain things I've written on my resume, and I had to quickly solve a programming problem.
A few days later, I received an email inviting me for an on-site interview at their Palo Alto offices. The process took the entire morning, ending early afternoon. I had to do three coding interviews back-to-back; thankfully, the interviewers were all extremely nice and friendly, and there was a snack bar nearby to keep my brain fed. The Palantir blog has a lot of tips on how to interview, and they came in really handy in helping me decipher the coding problems. I highly recommend reading through all the posts.
After the three interviews, I ate lunch with a Palantir engineer, and then some other Palantir engineer demonstrated to the morning batch of interviewees how Palantir software worked.
Side note: They were doing massive amounts of recruitment -- according to the shuttle driver, there had been about 20 people coming in every day for the past few weekends.