I was an employee referral, I had two on-site interviews at Gotham (NYC office). It took about two weeks to schedule the first on-site, which was three technical screens and one culture screen. I heard back within a week that there would be a second on-site follow-up with a hiring manager, which proceeded around two weeks later, also on-site at Gotham. I heard a week later there would be a third round, a conversation with a director. That happened over Skype within a few days. A few days later I received an official offer.
The process overall was positive if a bit long (seven weeks from first interview to offer). I got a good overview of the company and it's culture throughout and had a good view of what I was getting myself into.
Tips: what matters to Palantir is impact: focus on what you did in your last role (and even before that) and the impact that it had in your organization, on your customers, on your reports, on your product, etc. The interviewers (all of them) are very keen on detecting any sense of vagueness in answers--they will push you to be very clear, concrete, and reflective on what you did and it's outcomes. Have a solid story, and a solid understanding of it's impact and you'll do fine.
Technical questions are tough but not brain-teasers--reasonable implementation followed by average and asymptotic runtime analysis and algorithm/data structure improvement is the name of the game until you have the optimal implementation or you run out of time, not different from most companies. Also, they will ask about problem decomposition--be very clear with assumptions upfront, sketch out your approach, verify it with the interviewer, and move on with how you want to break down the problem.
Finally, be able to confidently and sincerely answer "Why Palantir?" The entire company cares deeply about this and square pegs don't fit in round holes: convince yourself before you sign on that it's the place for you.