Well...it's the usual stuff: testimony from "whistleblowers" and some photos that purport to show evidence. The idea of bases on the Moon, however, has a long - if not chequered - history. It began, as seemingly all such chequered histories begin, with famous 1950s contactee, George Adamski, who purportedly was recruited by the USA military to photograph UFOs on the Moon with his 6" 1nd 15" telescopes. Having done so, Adamski quickly concluded that they came from a secret base or bases on that planet.
Then the story mushroomed with George Leonard's Somebody Else is on the Moon(referenced in the article linked above), Don Wilsons' Our Mysterious Spaceship Moon, and a host of others.
But undoubtedly the grandfather of the Moon base hypothesis and all who came after him with variations on that theme, was Fred Steckling, an associate of Adamski in Adamski's later years, and the author of a real tour de force - or, depending on one's lights, tour de farce - called We Discovered Alien Bases on the Moon, recently reissued and revised by his son, Glenn Steckling. Regardless of one's biases toward the late Mr. Steckling, however, one cannot come away from his book without at least a glimmer of a suspicion that the idea might have some merit, for it is chock full of NASA unmanned and Apollo photos, and rare and hard-to-find information.
It was Steckling, for example, who first pointed out that Dr. Von Braun's statements to Time magazine in 1969, after the first lunar landings, that the equigravisphere was located at some 43,500 miles from the surface of the Moon necessitated a higher gravity for the Moon, and hence, an implied secret technology to get us off the Moon once we were there, and thus, it was Steckling who also first advanced the idea of a secret space program with alternative technologies: "The higher gravity on the moon means that an entirely new technology had to be used to return our Apollo spacecraft. The fuel required for lift-off from the Moon with these higher gravity figures, would have been astronomical.... It is very probably that the new electromagnetic technology was utilized since its discovery in 1965. From this appearance, the whole Apollo program was probably a cover-up for a super top secret space program."(Fred Steckling, We Discovered Alien Bases on the Moon II, p. 96).
It was also Steckling who popularized the little known writing and work of Maurice Chatelain, a NASA scientist in charge of Apollo communications equipment, and who openly wrote about the subject of UFO observation of the NASA space capsules. It was also Steckling who recorded and popularized another little-known fact, first mentioned by Chatelain, namely, that radios in France, Germany, Norway and Holland had picked up radio signals from the Moon, an incident that was kept "secret for some time."(p. 145).
While Steckling suffers from his association with Adamski, and from many of his assertions - surface water on the Moon or dense atmosphere for example - his collection of photos and information makes the book worthwhile. The only disturbing possibility that Steckling never really explores is the question posed by the title of the book: why does his "evidence" argue that the bases have to be alien? Nonetheless, if you want to inform yourself of the long history of the "secret Moon base" hypothesis, this is the book.