First, you fold the sheet in half and push the opposite corners into each other. Now the points of the fitted corners are the edges of a rectangle with the elastic edges folded inwards. Smooth out any wrinkles and finish folding the sheet. It will always be thicker than the flat sheet once folded, since the elastic adds bulk.
I’ve watched him do it, but the way he does it so fast is like watching those Japanese T-shirt-folding videos ;-)