Th general technique is called camera mapping, projection mapping, or videogrammetry. It works by taking a photo or video from an angle and projecting the image onto geometry.
As a simple example, think of a picture of a typical A-frame house taken from the front of the house. You could easily create the geometry of the house in a 3D application like Max, or Maya. You'd need a plane for the front of the house and planes for the sides of the roof and any dormer windows. If you projected the image of the house onto your plane and masked out the parts that were not house (the sky, ground, etc.), you could then move the virtual camera around it and it would appear you were moving around the front of the house in 3D.
Of course, as soon as you got far enough over to the side, you'd see there's no side to the house. So you'd need a picture from the side, and you'd need more geometry for the side of the house to project it onto.
In the case of a game like the Super Bowl they have cameras all over the stadium, and they know the geometry of the stadium, too. Mostly you just need a ground plane to project the field onto, and a rectangle for each player. Given that the field is green, you may be able to chroma key the players out from the field. You'll need to fill in where they were with at least something green.
There are tools to help with this. It's tedious, but in After Effects you can use lights to project footage onto a solid. There are also plug-ins to help, such as Buena Depth Cue's Camera Mapper.