Google posted the following video from an on air Google+ hangout in which a handful of the company's UX designers talk for about a half hour about the kinds of things they do when approaching user experience projects and issues. Included in the discussion are a YouTube designer, a Google visual designer working on the Chrome Web Store, and a UX guy from the Google Analytics team (he's also worked on the Google TV team and some of Google's ad teams).
The discussion starts off by talking about how putting the user first is Google's primary objective. The YouTube designer talks about how the UX staff put themselves in the mindset of the user and meet with the company's various product managers and engineers to push this element of things. They'll draw up mocks and prototypes on paper to illustrate things to the other Googlers.
A big part of their job is to work with other Google teams and talk to partners about where the user experience can be improved. The YouTube guy talks about meeting with partners at SXSW, for example, and collecting feedback.
Google+ itself has been huge for Google to collect feedback. Various Googlers are communicating with users throughout the social network, by hangouts and posts all the time. Even if Google+ never gets Facebook-like engagement from users, it's already proven to be an invaluable tool for communicating with Google itself. I don't think there are too many Googlers who aren't on Google+.
It's also good for just learning more about the inner-workings of Google - whether that's a random employee ranting about problems he has with Google's strategies, or discussions like the one in the video above.