As Armstrong descended the Lunar Module's ladder to the surface, he pulled a handle that opened an equipment bay on the LM. The TV camera was mounted on the bay and activated upon opening. There was no way to send the camera to the moon first and it's a good thing they didn't because Apollo 11 didn't land anywhere near the planned site. From http://www.solarviews.com/eng/apo11.htm ,

"Finally, about six and a half hours after the landing, they had the hatch open and Armstrong crawled out onto the porch - feet first and on his hands and knees. Moments later he was on the top rung of the ladder and pulled a lanyard to release a work bench / stowage area that was attached to the side of the LM. The Modular Equipment Storage Assembly or MESA was pivoted at the bottom so that, when Armstrong pulled the lanyard, the MESA swung down into a horizontal position. The most important piece of gear on it was undoubtedly the black-and-white TV camera. It was mounted in such a way that, when the MESA swung down, the camera was pointed directly at the foot of the ladder. For the astronauts, the landing had been the big moment of the mission. But, for the waiting world, the big moment was still to come - the first footstep.

From the bottom rung of the ladder, Armstrong had to make a three-foot jump down to the footpad - a contingency against a less than gentle landing that might have compressed and shortened the landing strut. From the footpad, he had only a couple of inches to step down to the surface itself. He stood on the pad for a moment or two, testing the soil with the tip of his boot before he made the epochal "small step".

The soil was very fine grained and had a powdery appearance and, once he stepped down, his boot sank perhaps a couple of inches, making a sharply defined print. Because of the Moon's relatively weak gravity field (one-sixth as strong as Earth's), Armstrong's total weight - half astronaut, half suit and backpack - was only about sixty pounds. Movement wasn't particularly tiring but because of the dramatic upward-shift in his center of mass caused by the backpack, he had to lean forward to keep his balance and it took a few minutes before he could walk comfortably. Just in case he had to end the EVA suddenly, Armstrong used a long-handed tool called the Contingency Sampler to scoop up a bit of rock and soil into a Teflon bag. He then removed the bag from the Sampler, folded it, and stored it in a shin pocket.

Aldrin joined Armstrong out on the surface about fifteen minutes later and then, for the next hour and forty minutes, the two of them examined the LM, moved the TV camera out about 50 feet, deployed a pair of scientific instruments, and collected more samples. One important set of questions to be addressed, of course, concerned the crew's ability to get the work done. If all went well, following crews could stay longer on the Moon, venture farther from the LM, and undertake more ambitious sets of tasks. For the first half hour or so, neither Armstrong nor Aldrin did more than a shuffling walk as they went about their work and it was planned, after this initial period of familiarization, for Aldrin to try to take advantage of the 1/6th gravity and try to run. Starting from near the LM, he first ran toward the TV camera, rolling from foot to foot in a loping or, as Jack Schmitt calls it, a cross-country skiing stride. Then as he turned and ran back toward the LM, he used the same gait again but twice changed direction by sticking a foot out to the side and pushing off of it, rather like an American football running back. Coming back toward the camera for a second time, he tried a kangaroo hop but decided that it didn't give him as much fore/aft stability as he got with the loping gait. It looked as though a crew that ventured a few hundred meters away from their LM would be able to run back in just a few minutes if the need arose."