At each corner, use your fingers to pinch the fabric together snuggly.....
----lazy me use sewing pins to hold the fabric together....you can tack it if you want.
Then I use the sewing machine to sew a straight line close to the pins. Careful to avoid the pins by removing them one at a time as you sew along.
Trim off the excess fabric at the four corners and the edges (if any)
Sew an elastic band all around the edges (depending on how much elastic band you have on hand, you can also just sew the elastic bands only at the four corners or at the top/bottom edges).
I've sewn the elastic band on the underside of the fabric for the 2nd piece so that it doesn't show on the right side...it does look neater this way I suppose. Voila...you've got a new fitted sheet....with a perfect fit!
I like to leave the excess fabric scraps for other small projects or you can use them for quilting.
I hope this sewing project can help you save some money from not having to buy so many bedsheet sets in future.