Sharpening scissors generally demands rubbing the beveled edges of the scissor blades against a rough surface which will hone down the edges to make them sharp again.
There are sharpening stones available for scissors and knives which you can purchase at retail stores, but there are easier (and more cost effective) ways to sharpen your scissors. In fact, there are several items found in most households which can be used to sharpen scissor blades.
First object is a glass jar, like a Mason jar or old jelly jar. To sharpen, open the scissor blades widely and place one on each side of the jar, one inside and one outside. Close the scissors until they are closed tightly around the jar at the pivot point of the scissors. Use constant and even pressure to slide the scissors back and forth like you are trying to cut the glass.
A screwdriver will do much the same, and the technique is similar. To sharpen, open the scissor blades and close them around the metal part of the screwdriver. Using the same even and constant pressure, try to cut the screwdriver shaft and drag the scissor blades backwards towards the tip of the scissors.
Sandpaper, aluminum, steel wool and an emery cloth will also sharpen scissors. The technique involves nothing more than using the scissors to cut through different textures of materials. In the end, the scissors will be sharpened. When using sandpaper, fold it in half so that both edges are being sharpened simultaneously. Cut the sandpaper into pieces and repeat. When using emery paper, do the same thing as sandpaper.
Quear, Charles Lorin Soils and fertilizers, for public schools;: A discussion upon the nature and treatment of soils and the value of fertilizers South Benn, IN: Printed By E.F. Harmon & Co, 1915. Print.
Walton, Harry How to Sharpen Everything Popular Mechanics Jan. 1965: 138. Print