Lots and lots of money thrown at it.
Essentially it’s the same concept as a green screen, where a computer will recognize certain colors and only overlay where it is supposed to.
But to make it work using the field which isn’t a nice bright uniform green they have to recalibrate the colors a number of times before the game and during the game. Selecting players uniform colors as stuff not to overlay, selecting the field colors which change depending on lighting, etc.
It does help that they also have position encoders in all the cameras so they can calculate what parts of the field are where based on where the camera is, where its pointing, and how far it’s zoomed in.
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