Well, you can use peroxide to wash the part of the animal where you think there is a mark of a spider bite. You can apply Neosporin on the infected region. You can repeat this process twice a day. You can cure this infection by giving any antibiotics to your dog.
Any antibiotic can make your dog feel perfect in a day or two. Another way is, just wash the infected place with soap frequently and your dog should be fine with in few days.