There are first aid classes for pets!

Your veterinarian can make recommendations.

Actually, most of what's in your human first aid can be used for the dog, with the big exception of ibuprofen and acetaminophen, both of which are poisonous to dogs. Aspirin will work; ask your vet for the dosage. (S)he may prescribe a pain med specifically for dogs.

Self-adhering foam veterinary wrap, sold in farm stores and many pet stores. is useful for keeping bandages on the legs. It can also substitute for elastic bandage for humans, with a few strips of duct tape on the outside for stiffening. You should replace it yearly because the material fuses to itself under heat and pressure.