For Feathers -
For a crib sheet cut 39 1/2" x 62 1/2" sheet fabric; seams 3/8" - cut 5" squares out of all four corners of your crib sheet fabric; with right sides together sew cut-out sections together to form corners to go over the mattress (serge, or sew and then zigzag); I then would fold over raw edges all the way around 1/4" and then again 1/4"; I would then take 1/4 inch elastic and start 6-10 inches from the corner and sew the elastic on the wrong side of the sheet stretching it as you sew from one corner to the next right on the 1/4" hem. I don't sew it all the way around the sheet, but you can if you prefer.
I would make them out of flannel and they fit perfectly. You can do the same thing and make cradle sheets the only difference is the size - large cradle 24" x 40" and small cradle 22" x 38" cutting out 2" squares in all four corners.
I never worried about anyone seeing the elastic as it is on the inside of the sheet next to the mattress. Very fast and fun. Always a big hit and if you are giving it as a gift with something else you can use the sheet as wrapping paper. Enjoy!