How does facebook know what I am googling or searching for outside of facebook?

[Ivolution]

Your hunch is incorrect, search information is not shared in that way.

Currently (September 2009), Facebook does not have any arrangement with Google or any other search engine that gives it or advertisers access to your search data.

How Facebook ads work is very specific and defined in detail on the site. Ads take advantage of user's willingness to share (usually) true information about themselves, such as gender, location, age, and even their marital status. Advertisers can select from a specific range of these, but they are all from within Facebook. As an advertiser, I can target, for example, users who list "model airplanes" in their interests or are a member of 1940 Biplane Club on Facebook, but I am not given the option to target based on searches or external sites such as Google.

(By the way, user information is not given to advertisers; the targeting is done by an automatic and anonymous system.)

See the source link for more information on how exactly Facebook ads work.