This one is probably going to be tough to communicate without diagrams. I don't know if my technique is optimal, but it's better than nothing:

At each corner of a fitted sheet, there will generally be a seam that goes a few inches in toward the center of the sheet and then stops. My technique involves holding/pinching the sheet by the inner ends of these seams, which allows you to fold along the relatively straight lines between these seam-corners, instead of using the curved elastic edges as your reference line.

Starting at one of the two narrower ends of the fitted sheet, grab the two seam-corners on your side of the sheet. Grab them from the top, not the bottom, so you can see your hands. Next, for each hand, while holding onto one corner, grab the adjacent free corner and pinch them together. This is your first fold.

Then, holding two adjacent corners in each hand, spread your arms out wide, flap the sheet until it mostly straightens out, and quickly fold the sheet a second time by bringing your hands forward and together. This is your second fold. Use one hand to hold the four seam-corners together, and the other to grab the sheet in the place you folded it.

After this the sheet should have a small enough area to fold like any other soft, mostly flat object, and you don't need to worry about where the natural corners are.