I applied online. After about a week I was scheduled for a 45 minute phone interview by the Recruiting Manager; we talked about my general background and technical knowledge.
A day after that they got back to me and scheduled me to have another hour long interview with the hiring manager, who was the Principle Product Manager; we talked about the specifics of the position, the expectations of the position, the work culture, more specific details about my background, etc.
A couple days after that they asked me to do a video-conference interview with the GM of Product; we had some high level discussion about software in general, my background, his background, the Product team at TTD, and some other general industry info.
And then about a day after that they asked me to come in for a full day of interviews with four members of the team, including the CTO, VP of Engineering, and two other senior members of the company. That full day of interviews was fairly daunting, but it ended up being mostly about the cultural fit and not technical prowess. That being said, the VP of Engineering did run me through a minor skills test to see how I would respond to one of the current problems facing the platform UI.