The whole process was wonderful. I had a very strict deadline before I had to decide on another offer, and Palantir catered to that very well.
It started with phone screenings, after submitting a couple of writing samples. I ended up doing 4 phone calls with members of the documentation team. After those were done, they asked me to complete a writing test and then flew me out to Palo Alto, where I interviewed with 4 people, had lunch, and then watched a demo. After that, I interviewed with 3 more people, and the next day after I returned home, I had a Skype call with a founder.
They paid for my hotel & transportation, as well as gave me food & drinks during the interview process. Everybody seemed extremely happy there, and very dedicated to the work they do. Their office is gorgeous as well.
The interviews weren't extremely difficult. However, they did ask me some basic questions about Java, HTML, and Actionscript (they don't use Actionscript, but they wanted to know how much I knew about it). I don't know if they ask that of all their candidates for this position, or only those who come from a more technical background. Many of the questions were more related to personality and problem solving. The writing samples I had to submit were taken highly into consideration.