For well over a century, philatelists have used small strips of adhesive paper known as hinges to mount postage stamps in albums. When remounting a stamp from one album to another, it's desirable to remove the old hinge before applying a new one to avoid a build-up of material. This presents no problem with modern hinges, which use peelable gum, but old hinges can pose difficulties.
Lay the stamp face down and tug lightly on the hinge with a pair of tweezers. If it's a modern hinge with peelable gum, it will simply pull away, leaving a strip of gum residue. (Don't wet peelable gum hinges, as this will only make them more sticky.) Once the hinge itself has been removed, you can go on to Step 3. If a light tug does not remove the hinge, then consider Step 2.
Use a cotton wool bud moistened with a drop of water to lightly wet the remaining piece of hinge. When it starts it buckle, tug on it gently until it begins to become dislodged. Repeat the process until the hinge comes totally free. You will still be left with some gum residue. If you wish to deal with this as well, then try Step 3.
Fetch a small sheet of transparent plastic. Breathe onto the stamp--as you might breathe on a pair of eyeglasses before cleaning them--then quickly lay the plastic sheet on top. Turning your tweezers around, rub the blunt hinge up and down the strip of gum, then peel away the plastic sheet. Most of the gum should have transferred itself to the plastic.
Removing an old hinge can be useful when reselling a stamp, as collectors like examples to be in clean, crisp condition on both sides.
Don't try to pass off a previously mounted stamp as an unmounted example, as keen-eyed collectors will in all likelihood spot the deception and want their money back. Instead, describe the stamp as previously mounted but showing little sign of it.