Daisy May shows up from ??? o’clock to noon on Sundays, in-game, wandering around your island as a funny little pig with a big ol snot bubble blowing out of her nose, hah.
She’ll sell turnips for X bells at that point.
Monday - Saturday, the store on your island (and others) will buy turnips at a set price. Like @Kolbex noted, that price changes at noon each day.
There are a handful of “patterns” for prices. Fluctuating, slowly decreasing, small jump, and large jump. Each week, your island will (mostly) randomly pick one of these patterns secretly in the background (there’s some modest math at work that makes it unlikely to keep getting the same result week after week and the like).
If you’ve got a decreasing pattern, womp womp, the best you can do is sell your turnips for a small loss first thing on Monday morning. But the problem is, the small and large jump patterns start out looking a lot like a decreasing pattern! D’oh!
There are websites you can use that will calculate the pattern you’re on and reasonably predict your max/min prices for the week after you can give it a couple weeks’ worth of data.
So, you can very easily invest heavily, wind up in a decreasing week, and lose money. Or only buy a few and trigger a big spike week and have nothing to sell!
Final thoughts on turnips:
You can visit others’ islands to sell. We used to be really good about posting our prices in this thread, but I think enough of us have cooled that it’s not super frequently checked anymore, sadly. But there are also websites where people post their Dodo codes if they have a good price (though getting onto and off of their islands can be a real hassle, since the whole game pauses for everyone everytime someone arrives or leaves. . . ).
If you fail to sell your turnips by the following Sunday, they rot and become next-to-worthless.
Not totally worthless.
It turns out that a certain bug really likes spoiled vegetables and will only show up for them. . .