Roll out a small amount of dough at one time. Keep remainder in refrigerator until ready to use. Roll dough on plastic wrap or pastry cloth. This prevents working too much flour into dough.
Extra flour can toughen cookies.
Choose simply shaped cookie cutters that are open in the back. Closed-back cutters can be difficult to work with as the dough warms up. Bake dough on sheets that don't have sides like jellyroll pans. If you only have pans with sides, turn them over and bake the cookies on the bottom. Side walls trap moisture and result in damp, soft cookies.