Ideas on how to cure my dog's red paws.

Rest your dog.
Inspect your dog's paws for injuries.
Treat your dog's paws with an antibiotic solution or anti-fungal solution.
Consider your dog's diet and potential food allergies.
Inspect your dog's regular physical environment for possible sources of allergy or injury.
Have your dog's paws inspected by a veterinarian.
Consider using a device to prevent your dog from licking it's paws until the condition subsides.