The winning team has not explained precisely how they came to discover the location of all 10 balloons, but the process detailed on the team website explains that they created a viral campaign to encourage people to put forward information they gleaned about the locations.
DARPA, the folks who laid the foundation for the innerwebs, is holding a contest as part of its efforts to study online behavior.
You can read the press release here (PDF). According to the press release, the balloons will be visible for one day only:
The 10 balloons will be placed in publicly accessible locations in the continental United States and will be on display for one day (December 5th) during daylight hours. The first participant to identify the latitude and longitude of all 10 balloons will receive the cash prize.
There is a $40,000 cash prize for the first person or group to locate all ten balloons.
The New York Times has more.