The elastic I use all the time for sheet making is a nice stretchy 1/2 inch elastic. on a large sheet, I usually just go about 18 inches both sides from the now-sewn-in corner and stretch a piece of elastic about that far - about 36 inches and then apply it to the edge of the sheet, starting eighteen inches from a corner, and ending up about eighteen inches from the corner.
Since I have finished the edge of the sheet itself with a turned under hem the elastic is applied to the underside (seam) side of the sheet.