Do not be concerned if your fitted sheet does not extend long enough to tuck under the mattress, because not all of them do.
Most sheet sets come with two sheets: the fitted sheet to cover the mattress and the flat sheet that goes on top of the fitted one. The fitted sheet is usually sewn with elastic that makes pockets on the four corners, helping it hug the corners of the mattress. The pockets keep the sheet from coming off the mattress during the night. Fitted sheets may have elastic on two sides or elastic all the way around. Purchase sheets designed for the size of mattress you have.
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Lay down your fitted sheet on the mattress and spread it out as flat as possible. Ensure it is going in the right direction, as the mattress is longer than it is wide.
Grasp one corner of the fitted sheet over the top right corner of the mattress, pulling it under the mattress. If there is a seam on the corner of the fitted sheet, it should end at the top of the mattress.
Slip the sheet over the corner at the foot of the bed on the same side. Tuck it under the mattress.
Walk around to the other side of the bed and slip the corner of the sheet on the corner of the foot of the bed.
Pull the sheet toward the top left corner of the bed and tuck it under that corner of the mattress.
Walk around the bed and ensure all corners of the mattress are still in place, tucked under the mattress.