Given a clockwise counting of corners, with the "outside" facing away from you (so you are looking at / reaching "into" the sheets from the elastic side):
grab the inside of 2, invert, shove into the inside of 1.
do the same for 3 into 4.
now you have a sheet folded in half, with two pairs of corners together.
grab the inside of 1+2, invert, shove into the inside of 3+4.
now it's folded to a quarter, and all the messy stuff is together.
lay out flat, straighten messy stuff a bit, so you can do the next step more easily.
grab the whole thing, chuck into the closet.
I never understood the need to fold bed sheets. Crinkled sheets simply aren’t a problem I’ve ever had; you barely notice the difference once they’re stretched over the bed and pillows. I have a blanket box at the end of the bed; I just shove the second set of sheets in straight out of the dryer.
(I do fold sheets for the guest bed but that’s because the alternative set might spend months on the shelf. Most of the time the same set is washed and put straight back on the bed.)
You fold them so you can stack them on other folded things. If they're messily folded, the pile falls over as you carry the basket upstairs, or stack other things onto them on your shelves.
For me bedsheets are their own wash cycle, so there’s nothing to stack them with. I just carry them upstairs and dump them into the blanket box when they're done. No need for a basket.
But let's say your washing process is different to mine. I'd still rather do two trips upstairs than fold sheets.
