the trouble is, the conspiracy buffs will tell you that unmanned craft put them there...
Fly an unmanned craft remotely to the moon and land without crashing, several second delay for "live" grainy video to come to earth respond and send signal back. Then leave all the bits behind, leaving various marks in the dirt and fly the craft off, successfully docking again via remote control. Then fly home and in an era when they best way to land on earth was drop them in a really big puddle.
Next part is easy. Set up a studio that looks remarkably like where they land on the moon, and transmit the actors playing their role. Can't do it in real time due to the "slow motion". So it must be prerecorded by at some reasonable time. Have all the actors leave bits in the same places as the remote control thing on the moon.
And nobody gives up the secret.
Reminds me of the movie Capricorn One