Have you ever tried to fold a fitted sheet and only experienced frustration?  Until I figured out the trick, I always used to end up with a bundled mess that I called "folded."  

The temptation is to match up the edges.  

However, if you have tried this, you know, it doesn't work.  As with the 12-step program adage, "The definition of insanity is doing the same thing over and over expecting different results," matching up the edges will always produce a bundled mess.  Let's not be insane.

folded sheet
Credit: wsm

Starting from the realization that the elastic in a fitted sheet drives a non foldable shape, we can look elsewhere for our standard, our ground truth as it were, the part of the item that defines the true shape of the material.  The key? What I like to call..

The true corner.

Credit: wsm

By matching up the true corners, the sewn portions that would set on corners of your mattress, you are using the most predictable shape inherent in the material.  You can find these sewn portions by searching along the elastic edge.  A seam perpendicular to the edge and ending less than a foot away from the edge indicates a true corner.  So once you find these true corners, fold your sheet as you normally would, using these as your guide rather than the sheet's edge.

Credit: wsm

As you can see, after finding the true corners, you can fold the sheet in half, then continue halfing the sheet until you finally end up with your folded sheet.  

Using the true corner method will produce a neat, compact fold that will allow you to even put the sheets back in the bag they came in when you purchased them.  To summarize:

1: Avoid the edge.

2: Find the true corners

3: Fold the sheet as normal, only using the true corners as guides rather than the sheet edge.