The area in the pad where the corn is will have a hard surround with a hard section protruding slightly above the pad. The area that protrudes should be trimmed off, and this is not difficult to do with the tip of one of the sharp snap off blade knives that are available in most hardware stores.

If you have a steady hand and magnifying glass, you can in fact trim down a little below the surface as you are trimming a dead area, and doing this will not cause bleeding or cause undue pain. The more you can trim out the better!

While this in itself will make it more comfortable for the dog to walk on, it will also expose the centre of the corn, and this will make it easier to kill the damn thing.

This is done by buying a styptic pencil at a chemist. These are an alum stick or aluminium hydroxide and are traditionally used by guys that are silly enough to cut themselves shaving to stop the bleeding.
Dip the end of the stick in some mentholated spirits and then apply this to the centre of the trimmed corn by gently rotating the stick.

Applied twice daily for four or five days will generally kill the corn by depriving it of a blood supply.

Hope this works as well on your dog as it has in the past on mine!

Tom