Good question.

I'll answer your question, with a question....

How do they retrieve the video footage that comes from the camera that is mounted onto the External Tank during shuttle launches?

The video signals are transmitted.
Camera on the rover was controlled from Earth.
You know they could broadcast television signals, radio waves etc? yeah?

Obvious answer - it was all fake!

That or the camera is on a tether. That's all I have!

How 'bout some upvotes with those comments, eh?

Goodnight Moon! See you tomorrow... or 50 or so years later!

Uhmn, at 0:22 in, does someone in the control centre comment 'I hear you have good thrust'? Exactly how closely to these nasa guys work together?

Imagine if they slightly underestimated the amount of thrust needed to escape Lunar gravity...

The scattering particles of foil from the lander make for a nice Star Trek-era special effect. It seems the R, G and B channels are sampled at different times and are not interleaved. I bet the lunar landing hoax crowd are having a good time with this one.

The video was shot from the lunar rover camera and transmitted from the lunar rover's antenna. With the time delay in sending commands to the Moon, everything had to be carefully planned in advance and the tracking had to be done blind. I have attached some quotes from a website below. (Sorry for the long post..)
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The only photograph of the lunar liftoff was taken from Earth and had expectedly poor resolution. "Gene tried to persuade me to stay outside and take a really good picture of liftoff, but I politely declined," Schmitt joked.

As the third outing drew to a close, Schmitt clambered up the ladder of the Apollo 17 lander. Alone on the moon's surface, Cernan steered their battery-powered automobile a mile from the spacecraft and parked the rover so a video camera could record their Dec. 14 liftoff. As he climbed from the vehicle, Cernan bent down and traced the initials of his 9-year-old daughter, Tracy, in the soil. Then he literally hopped and skipped in the moon's low gravity back to the lander.

For Apollo 16 and 17, however, flight controllers did track the ascent stage. With the punch button command arrangement and a 3 to 4 second time delay, their command sequence had to be totally preplanned. I had worked with Ed Fendell for the Apollo 17 liftoff to get it exactly right for a long tracking shot. At liftoff, the action was perfect, but soon the image of the ascending capsule drifted out at the top of the frame. Ed was furious that, after all the calculations, we missed the mark. It was discovered later that the crew had parked the Rover buggy closer to the Lunar Module than was prescribed by mission plan, and the vertical tilting of the camera was too slow.
Whenever I see a clip of that liftoff I note, as the stage nears the top of frame, a cut to a film shot of the stage ready to dock with the command module. And I still think, "Darn, we could have followed that final liftoff 'til it was but a dot of light winking out as it headed for the mother ship."

http://www.ehartwell.com/afj/Apollo_17_quotes