In this video, watch test pilot Graham Tomlinson keep the F-35B remain stationary 150 feet above the runway:
So how does it work? Inside the jet is a vertical-thrust fan, driven by a shaft from the engine. The entire thing is covered by a "lid" (you can see it behind the cockpit, raised, in the video), and small dorsal doors allow the engine to intake extra air for hovering, which requires considerable power to accomplish. (Naturally, the jet's exhaust swivels downward as well.)
The F-35B is slated to be used by the U.S. Marine Corps and British Royal Navy. The non-hover vesion, the F-35A, will be used by the U.S. Air Force and several international customers.
A third version, the F-35C, will be used by the U.S. Navy for carrier catapult launch and arrested landing.