Cut away any strings or strands of fiber sticking out where the scratches are on the leather. Use scissors for this step, and be careful. You want to cut away the strings and fibers as closely to the base as you can without further damaging your sofa.
Use a scalpel or razor knife to cut away any bits of raised leather in the damaged area. Again, be careful to cut away any damaged leather that is sticking up without further damaging your sofa.
Remove any leather that you could not cut away by sanding the damaged area with 320-grit sandpaper. Sand until the bits of leather are removed.
Prepare the damaged surface for filling by smoothing it with 1200-grit sandpaper. This may seem like a lot of sanding, but the sandpaper used in the previous step was to remove torn leather while the 1200-grit sandpaper in this step smooths the area for repairs.
Clean the area using an alcohol-based leather cleaner. Wipe the cleaner over the area, allowing it to air dry for 10 minutes before proceeding to the next step.
Apply heavy leather filler to the damaged area by spreading it over the scratches and punctures with a palette knife. The filler fills up the scratches to provide an even surface on the sofa.
Allow the filler to dry for five minutes. Sand the damaged area again with 1200-grit sandpaper.
Apply a coat of colorant to the damaged area with a sponge. Allow the colorant to dry, applying the second coat by sponge (if little coverage is needed) or by spray bottle (for blending colors or if more coverage is needed).
Evaluate the repaired area. If scratches are still visible, simply repeat Steps 6 through 8 until the area looks repaired.
Apply the sealant included in your colorant kit (this is most often a lacquer-type product). Allow the sealant to dry.