Conspiracy theories generally depend upon an absence of critical thinking. Any reasonable debunking generally requires critical thinking to cut through the misdirections, false assumptions and flawed logic upon which these theories are inevitably based.

Nevertheless...

To execute a hoax, there is need of means, a motive, an intended target, and some expectation of success.

Who would be the intended target of such a hoax? The American public? The Soviet government? The general public of the world? 

If the Americans had a motive and a target for a hoax, it would have been to make the Soviet Union think they had achieved a manned Moon landing without actually doing so. The snag here is that the effort to actually execute such a hoax (without it being discovered) would probably be greater than the effort to actually do it for real. Add to that the embarrassment should such a hoax ever be unmasked. The Soviets could easily tell if a radio signal was coming from a transmitter on or orbiting the Moon vs local to Earth. They knew what it would take to put a man on the Moon - they had their own lunar landing program (conducted in secrecy to avoid the embarrassment of a public  failure). The Americans could not realistically have executed a hoax without the Soviets seeing through it and calling them out.

The Moon landings occurred in the context of the Cold War Space Race. The Soviet Union, like the US, was developing nuclear bombs and the long-range ballistic missiles needed to deliver them onto targets pretty much anywhere in the world. As this was going on, the Soviets launched Sputnik, the world's first artificial satellite (which could be easily tracked by radar and even seen under the right light conditions, despite its small size). No question this happened. As the Soviets continued onward to put a dog and then a man in space, the US found itself trailing behind. As they were fighting their way back toward parity, Kennedy made his famous Moon speech. The intent was to get out in front of the Soviets and do so with a clear demonstration.

The purpose of the lunar landings was to put a man on the Moon as a show of technological superiority. The American effort was transparent in terms of what was being done, when, and why during each space mission, giving the Soviet Union ample opportunity to verify exactly what was really going on.

The Soviets would have liked nothing better than to disclose an American hoax if it indeed was one. The fact that the Soviet leadership congratulated the Americans on their success, rather than even suggesting anything was not as claimed, speaks to the fact that everything was exactly as it appeared to be.