Drakevarg
Troubadour
Years in my setting are shorter than on Earth (288 days to be precise), and they have shorter months as a result (12 months of 24 days each). The months have pretty basic names and honestly just keep track of how many full moons there've been (First Moon, Second Moon, Third Moon, etc). Chief exception being the final month of the year is instead called Thirteenth Moon (or Vlemma Pnevma, "Spirit Gaze" in Draconic) because it's the only time of year that both moons are full at the same time (normally they trade off, with one being full that month and then the other the next).
There are three main reasons for me bothering to keep track of this:
1) That way I don't need to use names derived from Earth's myths and history in my world that is clearly not Earth.
2) The interplay of the two moons has a significant impact on how the spiritual world behaves.
3) By making the need to keep an eye on that a fairly universal concern among scholarly types, I don't need to worry about coming up with 9 different names for each month based on the language and history of the culture in question - they're all going to be calling it essentially the same thing.
Days of the week are a bit trickier. Most cultures use an 8-day week, with the exception of the Fterota, who have a six-day week on account of using Base-6 math (their hands only have six digits). Conveniently enough (and actually unintentionally), this means apart from having four weeks to a month instead of three, their calendar works out basically the same otherwise.
I haven't put much thought into naming weekdays yet, simply because it hasn't come up. There's no particular mystical significance to weeks, it's just a convenient way to divide up a month into more immediately relevant chunks. And conversationally you can just describe things in a relative sense ("it happened X days ago" instead of "it happened last wheneversday"). That said, I know I'll need to get around to that soon, especially given my latest game design pet project, which WILL require me to let the player know what day it is. Still no idea what I'm gonna do for that.
As for explaining it all to the audience... I look at it the same way that I look at every other aspect of worldbuilding: if you treat it as an obvious fact in-world, the audience will either pick it up eventually or never get around to caring. And either way works fine. I don't need them to sit down and appreciate the detail work I put into things totally irrelevant to the story at hand.
There are three main reasons for me bothering to keep track of this:
1) That way I don't need to use names derived from Earth's myths and history in my world that is clearly not Earth.
2) The interplay of the two moons has a significant impact on how the spiritual world behaves.
3) By making the need to keep an eye on that a fairly universal concern among scholarly types, I don't need to worry about coming up with 9 different names for each month based on the language and history of the culture in question - they're all going to be calling it essentially the same thing.
Days of the week are a bit trickier. Most cultures use an 8-day week, with the exception of the Fterota, who have a six-day week on account of using Base-6 math (their hands only have six digits). Conveniently enough (and actually unintentionally), this means apart from having four weeks to a month instead of three, their calendar works out basically the same otherwise.
I haven't put much thought into naming weekdays yet, simply because it hasn't come up. There's no particular mystical significance to weeks, it's just a convenient way to divide up a month into more immediately relevant chunks. And conversationally you can just describe things in a relative sense ("it happened X days ago" instead of "it happened last wheneversday"). That said, I know I'll need to get around to that soon, especially given my latest game design pet project, which WILL require me to let the player know what day it is. Still no idea what I'm gonna do for that.
As for explaining it all to the audience... I look at it the same way that I look at every other aspect of worldbuilding: if you treat it as an obvious fact in-world, the audience will either pick it up eventually or never get around to caring. And either way works fine. I don't need them to sit down and appreciate the detail work I put into things totally irrelevant to the story at hand.