So start off measuring your mattress. Mine is 36 by 15. then add a quarter inch to all sides for ease. So 36 1/2 x 15 1/2. Measure how deep the mattress is: 2 inches, and add enough extra to fold under, at least another 2 inches, plus 1/4 inch seam allowance. so that adds up to 4 1/4 inches to for the sides. Add that to all sides of your top measurement so your final total is 45 x 24. Cut a square of this size out of your fabric. with the yardage I had, I was forced to add a small strip to the long end to make 45 inches. Try to avoid it, but if you must piece your fabric, either serge, zig zag, or french seam to avoid fraying during frequent laundering. Also, if you must seam, try to either hide it, or put it somewhere where it won't look so bad. Mine is hidden down the side of the mattress, but what about adding a 1" stripe of contrast fabric a quarter or a third from the end of the mattress? Or put a flat felled seam with contrast stitching a quarter or a third of the way down the mattress. That would allow you to cut in two pieces, and in some cases, save fabric.
Add up all 4 sides of the top measurement of your mattress (36 1/2 x2 + 15 1/2 x 2 = 104) add two inches, and cut enough strips 2 inches wide from your fabric to meet this measurement. (my fabric is 42 inches, so I need three strips.)
Take your large rectangle, and in each corner, mark a small square the depth of the side (4 1/4) less 3/8, so for mine, 3 7/8, and cut it out.
then pin the corners together wrong sides together:
Sew at 1/8, and press flat:
then turn so that the right sides are together, and sew at 1/4. This makes french seamed corners that will survive many washings.
Now take your 2 inch strips, and sew them together to make one long strip. Press that strip in half. starting about in the middle of one of the long sides of your sheet, line the raw edges of the strip up with the edge of the sheet, with the strip along the right side of the fabric. Sew it on folding the edges under at the beginning and end, and trimming off any excess.
Then iron the strip to the wrong side, enclosing all the raw edges, and topstitch it down, finishing your casing. Add elastic, and you're finished!
The cradle looks pretty spiffy with the new sheets!
I've used the same method for making a changing table cover, using a pieced and quilted top, and a drawstring instead of elastic. You could also make basket liners using this method.
If you have leftover fabric, check your library for books on sewing curtains. It's dead easy, although not entirely intuitive. I have an excellent book from better homes and gardens called "sewing for your home" it's older, so the pictures might give you a giggle (think avacado, burnt orange, and shag carpets) but it's a great overview of the subject.