Ideally, a response with a time period before 1900 would be appreciated; but 20th century beliefs are fine.
If you want a good idea about what people thought the moon looked like before we went there, you should check out the Tintin comic Explorers on the Moon, published in 1954. The writer of the comic, Hergé, was very diligent about doing a lot of research to try and depict the foreign locales of his comics as accurately as possible (this was largely due to his experience getting to know a Chinese person while writing The Blue Lotus, and realizing that all his stereotypes about China were wrong).
The landscape that Hergé depicts is similar in color to the real lunar landscape, but he portrays it as much more craggy than it is in reality. Another notable misstep is including huge caves with stalactites and stalagmites, which obviously doesn't exist on the moon. He also portrays caves filled with ice that Tintin and his dog Snowy slip around on, though one might argue this was an example of him being prescient :).
While much of the technology portrayed in the comics is fanciful (the vessel was a gigantic one-stage V2-looking rocket that maintained artificial gravity by continuously accelerating), for some of the things he got amazingly close. The space-suits for instance, look fairly similar to the space-suits used by NASA, being big balloon-looking pressurized suits with a big domed glass helmet and a backpack (though his were orange, not white). He also accurately depicted the "hopping motion" astronauts used to move around, and showed what it would look like to drink whiskey in zero gravity (remember, no one had actually been in space at this point, so the fact that he knew to draw the liquid as a sphere and that he accurately portrayed how humans look is fairly impressive).
I should say that this is basically the extent of my knowledge about pre-Apollo portrayals of the moon. I'm not a historian, just a guy that really, really likes Tintin. I hope this suffices as a top-level comment, given that I think it's a pretty fascinating portrait of how one writer imagined what a realistic trip to the moon would look like.
Edit: here's an album of Destination Moon/Explorers of the Moon scans I made a long time ago for another purpose, and just remembered. It contains a lot more detail than the pictures in the rest of the comment.
Edit 2: Thanks for the gold, anonymous user!
I clearly remember a cartoon from around 1968 where an astronaut discovers that the moon is not made of cream cheese but is actually Roquefort.
People may have joked about the moon being made of cheese, but no one actually believed it, anymore than trekkies believing that the universe is filled with aliens that look a lot like humans with funny hats.
In A Textbook of General Astronomy (Charles Young, 1889) the ideas about the moon are pretty close to reality. Even Galileo could see that the moon was a lot like an airless desert with mountains.
The biggest worry to the astronauts was how deep the dust would be. That's why Armstrong was quick to report that they had not sunk in very far.
One big surprise was the smell of the moon. Lunar astronauts reported that after a moonwalk it smelled like spent gunpowder, as if someone had just fired a pistol.
hi! not sure how far back you want to go, but you may be interested in responses in these posts
You might be interested in this post: "Was there a religious opposition to the moon landing and space program at its beginning".
Specifically, /u/jumpstartation's comment gives an excerpt from Andrew Chaikin's A Man on the Moon explaining that when Apollo 14 astronaut Stu Roosa visited Nepal in 1975, he discovered that some Nepalese believed the afterlife is on the moon.
(As an aside, I was so excited that I could finally answer a question here, then saddened when I realized that the only reason I had an answer was because I read it here already.)
At least one religion, the Mormons, had specific beliefs about the moon and its residents:
The inhabitants of the moon are more of a uniform size than the inhabitants of the earth, being about 6 feet in height. They dress very much like the Quaker style and are quite general in style or the one fashion of dress. They live to be very old; coming generally, near a thousand years.
This was based off of a description that the Mormon prophet Joseph Smith supposedly gave to Oliver Huntington. Although we only have Huntington's 1892 account of it, it was picked up and published in the Young Women's Journal in 1897. And the Millennial Star published similar ideas about an occupied moon in 1882. This all stems from passages in the Mormon scriptures, specifically the Book of Abraham that refers to other planets as inhabited. To the 19th century Mormon theologians, if there were other inhabited "planets" it was hard to imagine that the moon wasn't.
This idea lingered for quite sometime within the church. Even as late as 1961 Mormon leader Joseph Fielding Smith said the following:
We will never get a man into space. This earth is man’s sphere and it was never intended that he should get away from it… The moon is a superior planet to the earth and it was never intended that man should go there. You can write it down in your books that this will never happen.
And he wrote something very similar in his book Answers to Gospel Questions.
This is a vanishingly rare belief in the post Apollo era. Joseph Fielding Smith openly admitted when interviewed after Apollo 13 that he had been wrong. But there was (and still is) a small group of Mormons today that use the previous statements as proof that the moon landings were a hoax.
As OP is interested in older beliefs, I would like to ask: How about right before the moon landing? What were they expecting? Was water considered a possibility? Valuable resources? What expectations and hopes did the moon fail to meet?
Returning astronauts were put in the Mobile Quarantine Facility when they were picked up after splashdown so they could be observed for any illness/viruses/whatever that they may have caught on the moon, and so that it wouldn't spread.
They weren't sure what the surface would be like. They thought it would be either very hard from volcanic activity, or very soft, deep, and sand-like from meteorite impact (known in the biz as lunar regolith, a.k.a lunar soil). Hence the big footpads on the Lunar Module.