Clean the surface of the luggage needing repair, or better yet, if you can, clean the entire luggage. Use a compatible cleaner for the material your luggage is made of. For instance, you need a leather cleaner for a leather luggage. At the very least, if no specific cleaner is readily available, use soapy water. Apply the cleaner in small amounts using a rag, then wipe each part clean prior to moving to another section.
Prepare your repair kit. In case you don't have a ready repair kit to use, gather the following materials: rag, scuff remover (for a scrape or scuff) or a leather sealer that matches the color of your luggage (for a tear). You may also use a fabric glue, rubber cement or vinyl cement, depending on the type of luggage you have. Repairing a scuff requires applying the scuff remover and wiping it clean with a rag. Repairing a tear requires applying the leather sealer and working on the solution over the damaged area outwardly. Polish and rub the torn area until the solution becomes barely visible.
Apply a luggage conditioner or polish to the repaired area of the luggage. This is typically a part of most luggage repair kits available in the market. Polish and rub in small amounts per section. This brings back the luster and shine of your luggage, while also working as a sealer that protects the repaired part from further wear and tear.