Cut or scrape off any rough or frayed edges on your snag.
Apply a sub-patch to the snag if it is necessary to help level the snag with the rest of the fabric. A sub-patch is attached with leather adhesive. Do not iron on a patch, as this can damage the leather.
Apply leather filler to the snag. Leather filler is, according to Leather World Technologies, a water-based acrylic paste. It's best to apply the filler in thin coats, drying them with a hair dryer one at a time, until the snag is the level you need.
Clean the area around the filled area with a scuff pad and leather cleaner.
Use leather dye to recolor the filled section the right color. This will be less noticeable, if it's noticeable at all, than a surface patch.
Follow your recoloring with a coating of leather protectant over the entire piece.
Use a few dabs of clear nail polish to smooth down a small snag in your leather. This will prevent it from coming up.