Last week Elisa was organizing her linen closet and made the comment that she had given up trying to perfectly fold her fitted sheets. I agree that they are a pain to get smoothed and flattened into something that neatly fits onto the linen closet shelf. That is why years ago I started folding my sheets into nice little packages -- the fitted sheet and pillowcases swaddled tightly within the flat sheet -- so that one just has to grab a "package" to have everything necessary to put clean sheets on the bed (even a husband can do that in the middle of the night!). If you don't have sheet sets per se -- i.e. a matching set -- you will always need a fitted sheet, pillowcases and a flat sheet for every bed, so pair up your odds and ends as much as possible and make some "packages."
It helps to have pulled the sheets from the dryer just as they are dry and not to have a wrinkled mess to fold. That is a very important first step. So if you forgot about them and they sat for the night or several hours during the day, do yourself a favor and run them on a wrinkle release cycle (or about 10 minutes) and then pull them out when they are pliable.
Take the fitted sheet and fold in half crosswise (with a twin sheet you will have almost a square then) and fit the corners into each other -- take a minute and really work at it. Then fold again crosswise so that all the corners are in the same place and, again, fit them as neatly as possible into each other. It's very helpful to have a surface on which to lay the sheet at this point -- the sofa or a table. You need to be able to smooth the sheet with your hands against a firm surface.
With your hands, smooth the flat part of the sheet and straighten the elastic edge as much as possible. I admit that these sheets (which were my own teenage sheets) do not have a lot of elastic and sheets today often have elastic around the entire edge. Just straighten them as much as possible and smooth. The elastic will be hidden inside, so work at having straight outside edges.
Now fold the top part down so that the elastic edges are tucked inside the folds. You will have a long rectangle.
Now fold one end over itself several times until you have a rectangle.
Fold up the pillowase(s) and lay them on top of the fitted sheet.
Now take your flat sheet and fold in half crosswise. Then fold in half crosswise the other way and fold in half again the same way, so that you eventually have a long rectangle. Each time you make a fold, make sure your edges are together. You will be amazed at how easy it is, if you just take a minute to do it carefully. You can just imagine me saying to you, "Slow down...what's your hurry?" ;-)
Now take your stack of fitted sheets and pillowcases and place them on the end of the flat sheet rectangle that has the unfolded edges (the other end will have been the edge you folded first). Place the fitted sheet so that its neatly fold edge is on the same side as the neatly folded edge of the flat sheet.
Now start with the end that has the stack of sheets and fold so that you are essentially rolling the stack of sheets inside (except instead of rolling you are sort of flipping them over and over while keeping the stack firmly inside) until you have a nice neat rectangle and the sheets are swaddled tightly inside.
Now you have a nice neat little package to place on the linen closet shelf.