A dog's paw pads are tough, but they can get scraped, leaving them red and sore. This may happen when a dog runs and turns suddenly, when he's exercising on hard, rough surfaces or if he treads on a sharp object. Minor grazes can be cleaned and protected at home, but deeper lacerations should always be seen by a veterinarian.
Rinse minor abrasions in clean cool water or with a weak saline solution -- never rub the wound -- and apply an antibacterial solution or ointment to the affected area. The graze can be protected with a non-stick Telfa pad and a vet wrap or ACE bandage lightly wrapped around the dog's foot. Alternatively, cover the injured paw with a commercial boot or thick sock tied loosely above the hock joint for a back leg or above the elbow with front legs. Don't use elastic bands as they can interfere with the dog's blood supply. Bandages and socks should be kept clean and dry -- cover with a plastic bag if the dog has to outside in the wet -- and be changed daily. A pad injury should have healed properly within 10 days; if the pad isn't healing quickly, see your veterinarian.
Other than superficial grazes, pad injuries should be seen by a veterinarian as flaps of hanging skin and cuts are likely to need stiches. If the pad is bleeding badly, wrap a large piece of clean cloth around the paw and hold it firmly in place to help stop the bleeding while the dog is taken to the veterinarian.