So, based on those dimensions, you have a standard fitted sheet cut with approx a 7 inch mattress depth, 3 inch tuck under and 1/2 inch seam allowance. (Give or take)!!
Best to do a "french seam" when you sew those corners together, then it won't ravel when you wash the sheets. Start with your elastic on one side, and pull and stitch the elastic all the way around the sheet (not just on the corners) and when finished you will have a gorgeous sheet with all the edges covered and finished looking. Also they stay on the bed better and tuck under the mattress better.
Needless to say, if you are working with a full size sheet and making it into a twin, you would be able to have more coverage (mattress depth) on the sides and more to tuck way under the mattress.
A couple of years ago I googled and found a wonderful diagram and description of how to do this when I was in Australia. However, try as I might I can't find it right now. There are several but seem pretty confusing to me.
Obviously, the bigger the top sheet that you are cutting down, the more you will have for depth of your mattress and tuck under. Some of the newer beds have a depth of 9 to 11 inches and then need at least 5-6 inches to tuck under. With that in mind, you would need to cut out squares in the corners of 14 to 17 inches give or take in order to have full coverage and a generous tuck under.
This is my FIRST tute, I hope it made sense. Let me know if you have any more questions. Sorry it's not very spiffy!!