Grab a canvas fabric patch between the pinchers of your tweezers.
Stick the tip of the tweezers through the hole and release the patch. Enlarge the hole slightly if need be to make an opening large enough for the tweezers and patch to fit.
Smooth out the patch with the tweezers, adjusting it so that it lays flat behind the damaged area.
Insert the tip of your glue applicator between the patch and the leather, and squirt a small, even amount of adhesive all the way around the perimeter of the patch.
Let the glue set, allowing the patch to properly adhere to the back of the leather.
Dab leather filler on your palette knife, and smooth an extremely thin layer of the product over the hole. You want just enough to use just enough filler to make the patched area level with the leather on the rest of the couch.
Hit the filled area with a blast of heat from a hairdryer. Blowdry until set and hard.
Disguise the repair by applying a leather recoloring product over the area with a cotton swab. Select a product that the rest of your couch perfectly, otherwise the repair will not be seemless.
Prevent the leather around the repair from shriveling or wrinkling by applying leather conditioner all over the couch with a sponge. This keeps the couch maintained, preventing desiccation of the leather that can cause shrinkage and shriveling.