This is, I think, the flakiest of the major conspiracy theories. The basic conspiracy theory states that the moon landings were faked. There are variations - most insist that ALL the landings were fake, a few admit there may have been later landings, but insist the first landing was definitely fake. I'm not going to waste a lot of time on this one. Anyone convinced by this garbage has such poor critical reasoning skills that they are probably beyond my reach. What I'll do, instead, is provide a couple of videos which deal with most of the important points raised by the cranks.
PS - on a personal note, I have witnessed the 'reflected light' experiment which uses an array of reflective array, placed on the moon by astronauts from the Apollo 11, 14 and 15 landings. This basically measures the distance to the moon by firing a powerful laser at the moon, hoping to hit the reflective array and bounce some photons back to Earth. The time taken is an effective and accurate (to within a couple of millimetres) measure of the distance travelled.1 Whilst this experiment is possible without the reflective array, getting a reflection is so unlikely that it can take months to get a single reading. With the array in place it is still a tricky problem2, but a reading is possible on most occasions.
1 Distance = speed × time. Since speed is known (c=speed of light=300000000 m/s, more conveniently written as 3x108ms-1), then all we need is the time taken. We then simply multiply the time by 3×108 to give the distance. 2 Approximately 1017 photons are fired at the moon. This produces a beam about 7 metres wide at the moon surface. The detector needs only a single photon to take a reading. The task of hitting the reflector is compared, by scientists, to hitting a moving dime (UK - a 5p piece) with a rifle shot, at a distance of 3 kilometres.