First things first, as I'm big on definitions, I should define "cosmology".
Cosmology: 1) "The study of the universe as a whole, of the contents, structure, and evolution of the universe from the beginning of time to the future." (As always, retrieved using the google "define" function)
That first one's a little dry, though accurate. I prefer #2: "ideas about the universe as an ordered system and the place of humans in the universe."
To be fair to elves, dwarves, gnomes, fairies, and the like, we're going to change the word "humans" to "people". Cosmologies are big. Really big. You won't believe just how vastly, hugely, mind-boggling big they are.
Sorry, sometimes I channel Douglas Adams.
My point, however, is that the real information about the cosmology of a fantasy universe is often small, because it is limited by what people can perceive. Without a telescope, it's hard to see stars as more than little dots of light in the sky at night.
My family and I used to do medieval reenactment, and my mom told me this story. She once knew a man who would "get into character" at medieval reenactments by simply removing his glasses. He was very shortsighted, and he said that it helped to remind him that his persona had, and I quote "never seen the sky."
To me, the idea of not being able to see even the sky is very powerful. I want to keep this sort thing in mind as I design this cosmology.
It's going to be pretty sparse. We don't really need much, because most people can't really see much. There might be a crazy wizard in a tower with a magic spyglass, but that wizard is called crazy because most people think she is.
So, lets start with what we can see. In the day, there is a great sun in the skies. Just one, nice and simple. We're going to call it a red giant, because I don't want everything to be the same. There is a great red ball of fire in the sky during the day (Goodness Gracious!).
In the night sky, there are many small points of light, called stars. There are two moons, the greater and lesser. The greater moon orbits the world, the lesser moon orbits the greater moon. I'll determine the exact schedules some other time, it's not really that important. I'm not really sure if the moon having its own moon really follows good astronomy, but it's a fantasy world and I don't care.
This'll have some sort of effect on calendars. Probably something fun like having the greater lunar cycle determine the length of a month, and the lesser lunar cycle create weeks. Various alignments of lunar cycles can also create some funky tide options, but I'm not really going to get too deeply into it. I want to leave interesting alignments happenstances for dramatic occasions.
What do people believe the stars really are? Ask a thousand people, and you'll probably get a thousand slightly different answers. I'm not going to cover those here, I'm going to cover things like that in the posts about individual cultures. You might have noticed a theme here. I really, really don't want to pin things down so tightly that the world can't evolve if necessary.
I almost forgot to mention, the planet is spherical.
That's all for now, folks!