If the cut is small and shallow, you can probably take care of it with your cat's first aid kit. You'll start by trimming any excess fur around the wound. Then clean the wound the best that you can by using an antiseptic wash. We recommend getting a feline wound wash to have on hand ahead of time. Only use hydrogen peroxide sparingly and for short periods, as it can eat away more healthy tissue than necessary.
Allow the affected area to dry completely. Then apply a triple-antibiotic ointment like you probably already have in your medicine cabinet.
Using a non-stick dressing, place it on the wound, and layer it with bandages. Place another layer of cotton on top and cover it with a bandage. Use surgical tape to secure the dressing lightly. Then cover the tape with a self-adhesive bandage like vet wrap. After 24 hours, remove the bandage. If it hasn't started to heal, call your veterinarian.
If the wound is in an un-wrappable location on your cat, consider using Vetbond liquid bandage or another cyanoacrylate super glue to bind the tissues together without bandages. In a pinch, we've found cyanoacrylate superglue in Walmarts and dollar stores practically everywhere. Just be sure not to get it on your fingers!