An old remedy that has long been used when farm animals get a cut, after washing the area (degree of trauma dictates), sometimes hydrogen peroxide is for initial flushes then drying the area and bandaging (elizabethan collar can help with some pets) is all that is needed. But if there is a deeper puncture associated with it (horse steps on nail, dog cuts foot on piece of wire, etc) then soaks with epsom salts are handy. An old rain boot can be used for this. Wash out and then put in a double handful of epsom salts and warm water. Put the dog's paw into it and give chest scratches and ear fluffles for about five minutes, then dry the foot and loosely bandage.

I have also used a ziplock lock bag for the Epsom salt treatment.

A friend of mine Down Under had a dog get badly cut on the beach. The vet at the local clinic (a beach she was visiting) did some stitching on the dog but the dog had reaction to the stitches. After a week or so there was no healing progress, there was puss leaking out of the wound and constant drainage. The vet for some reason was no help at all and kept blaming her for not keeping it clean (at home, the dog lived inside the house). So my friend, (also a horse owner but she has to board) opted for the epsom salt soaks 2x a day and in a few days the stitches were cleaner. She cut the stitches out so the inflammation would go down further and in a few days time, the dog healed up just fine. This was a large breed dog over ten years old.

Antibiotics for punctures are usually "a given" (dog fights can result in deep punctures). Some dogs that are not usually exposed to dirt, squeaky clean environment, the usual flea / chemical exposures of home living and have lived on commercial foods their whole lives, often do better if they are taken to the vet and also given antibiotic prophylaxis along with care for the injury. This has to do with a weakened immune system/immune compromise. So in some cases, older dogs, younger dogs, sensitive ones -- may sometimes need antibiotics.