Writing in Slate, Ken Jennings describes what it was like:

[A]t IBM’s Thomas J. Watson Research Lab, an Eero Saarinen-designed fortress in the snowy wilds of New York’s Westchester County, where the shows taped last month, I wasn’t the hero at all. I was the villain.
This was to be an away game for humanity, I realized as I walked onto the slightly-smaller-than-regulation Jeopardy! set that had been mocked up in the building’s main auditorium. In the middle of the floor was a huge image of Watson’s on-camera avatar, a glowing blue ball crisscrossed by “threads” of thought—42 threads, to be precise, an in-joke for Douglas Adams fans. The stands were full of hopeful IBM programmers and executives, whispering excitedly and pumping their fists every time their digital darling nailed a question. A Watson loss would be invigorating for Luddites and computer-phobes everywhere, but bad news for IBM shareholders. …

I expected Watson’s bag of cognitive tricks to be fairly shallow, but I felt an uneasy sense of familiarity as its programmers briefed us before the big match: The computer’s techniques for unraveling Jeopardy! clues sounded just like mine. … Indeed, playing against Watson turned out to be a lot like any other Jeopardy! game, though out of the corner of my eye I could see that the middle player had a plasma screen for a face. Watson has lots in common with a top-ranked human Jeopardy! player: It’s very smart, very fast, speaks in an uneven monotone, and has never known the touch of a woman.

From the first night, including some biographical material:

On night 2, Watson gets 13 questions right in a row before anyone else can answer: