Sharpen scissors only if they’re very dull. Frequent touching up whittles away too much metal, causing the blades to cut poorly; professional adjustment may then be necessary. Before you decide to sharpen, tighten the pivot screw holding the blades together. (If the scissors are held by a rivet, slightly spread the rivet head by striking it with the ball end of a ball peen hammer.) If this improves the cutting, there’s no need to sharpen.
To sharpen the dull edge of a scissors blade, use an aluminum oxide bench stone (whetstone), available at hardware stores. Clamp the stone in a vise, coarse side face up. Spread light machine oil on its surface, then open the scissors wide and, firmly holding one blade ad handle, place the other blade on the stone, with the inner face vertical. Tilt it slightly less than 10 degrees so that the cutting bevel is flat against the stone; repeatedly move the blade diagonally across the stone (in the direction of the arrow) until you have the desired edge. Repeat on the other blade. Wipe both blades clean with a soft cloth: open and close the scissors several times to remove the thin wire edges that result from the sharpening. Leave the removal of deep nicks to a professional knife grinder.