Dan Russell of the Search Quality team has written a post on field studying user search behavior. The role of "user experience" research is to try and get the inside story on what people do when they search. We're constantly asking: What's the user's experience of search? What works and doesn't work for them? What are they looking for? What DO they want?
There's also a disparity between what they searched for and what they remember searching for later on.
Another area Russell dives into is eye tracking. Here's a video showing the eye tracking of 3 different people searching for "school backpack."
Last but not least, Russell explained the discovery that the "Advanced Search" page was really turning searchers off. They often were so overwhelmed or uninspired by the options, that they left the advanced options blank. They used that information to re-design the Advanced Search page.