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.