Measure the dimensions of your Pack 'n Play or a similar playard mattress. Standard Pack 'n Play mattresses are 29 inches by 37 inches, but other brands can vary. The sheet needs to fit tightly for safety, so it is important to get an accurate measurement of the mattress.
Cut a rectangle of pre-washed fabric measuring 16 inches longer in each dimension than your mattress. Old flat sheets can make great Pack 'n Play sheets, or you can pick a fabric that matches your design scheme.
Cut off an 8-inch square at each corner of the fabric. This is most easily accomplished by folding the fabric in quarters so all the corners are together, and then cutting all four layers at once.
Sew the cut edges in each corner together with a straight stitch. To do this, fold the sheet so the patterned side is in the middle and you see the reverse, and line up the edges you had just cut in a corner. Your stitch should be about 1/4 inch from the cut edges.
Fold over 1/4 inch of the edge of the sheet and iron it all the way around. Then fold over another 3/4 of an inch and iron it as well.
Sew around this hem using a straight stitch 5/8 inch away from the edge of the sheet to make a casing. Leave a few inches open in the corner so the elastic can be added.
Thread the elastic all the way around the sheet in the casing. It is easier to thread if you attach a safety pin or other rigid object to help pull it through.
Sew together the two ends of elastic, and then sew the last bit of the casing closed.