I read a factoid in a book last night that said if you were standing at the bottom of a well, you could see stars (other than the sun) in the daytime sky. Is this true? If it is, how?
I suppose if you fell down the well, you’d certainly see stars;)
This is a myth. The atmosphere scatters (reflects) light from the Sun, so even if you could block out the disk of the Sun, (as by going to the bottom of a mineshaft or well) you’d still see blue sky.
If this myth were true, I’m sure astronomers would hire lots and lots of grad students to dig holes. 
Now, the trick would work on the Moon, since there’s no atmosphere. If you just stand on the surface, the glare from the Sun itself, as well as sunlight reflected off the ground and the rocks and stuff would be much brighter than the feeble light from the stars. (This is why you don’t see stars in the pictures astronauts took on the surface.) However, if you dug a deep hole, you could block all those sources of glare, and then you could see the stars even in daytime.
No. See The New Scientist for origin (as far back as Dickens) and explanation.
But if you use a telescope you can see some stars. If you magnify the sky a lot, the scattered light is stretched out to a larger area, whereas stars are pinpoints of light and don’t get any larger. Of course stars aren’t perfect pinpoints due to limitations of the sky and telescope so there is a limit, but you can pick out some of the brighter stars. If you manage to point the telescope at a star, that is.
I’ve never heard the story with respect to a well, but I have heard the story with respect to a place in Australia. Supposedly there is a very deep and narrow rock cleft or cavern or something like that, from the bottom of which you are supposed to be able to see the stars during the day. I wish I could remember the name of the place.
Although you can’t see stars in the daytime, you can occasionally see Jupiter…but it ain’t easy. (IIRC, sometimes it’s about twice as bright as the brightest star). And of course, there’s Venus & Mercury at dawn/dusk…but at those times, some stars may be visible too.
And then there’s the moon in daytime (worth mentioning here since many people do not realize that the moon can be visible in daytime).
Is that like the desert in Mexico where gravity is different?