Open the scissors so the blades are separated. Hold the scissors in your dominant hand. The first blade that you're going to start sharpening should be pointing downward.
Hold onto the sharpening stone in your non-dominant hand. Sharpening stones of every size can be purchased from a home improvement or hardware store.
Slide the stone down the length of the blade from the pivot to the point (the pivot being where the two blades intersect; the point being the tip of the blade). Do this several times. Always count how many times you slide the stone down the blade to ensure they other blade gets the same amount.
Flip the scissors around so you can begin sharpening the other blade. Again, make sure that the second blade is pointing downward. Repeat Step 3 with the second blade, using the same amount of stokes.
Open and close the scissors quickly. The open/close motion will knock off any burrs from the blades.