There is no home remedy for fleas.
In order to save your dog you need to fumigate the house and yard: fleas do not live on dogs. They jump on when they want a blood meal. Then they jump off and find a mate and lay their eggs in your carpet and inside your box springs and the underparts of your couch.
You go to the pet store and buy a set of flea control products. Pick one that is water-based (so it won't stain your furniture) and contains an IGR (insect growth regulator) so you won't have to do this all season.
You will need a spray for the yard, a spray for the dogs, possibly a different one for your cats (if any) (check the labels), and foggers for your house and cars. Follow all the instructions on the labels EXACTLY: you are dealing with poisons.
DO NOT use any flea collars with the above package; it can overdose your dog and possibly kill her.
Note that this is not just for the comfort of your dog. Dogs get tapeworms from fleas, and fleas do carry some diseases. Fleas will bite people; if the dog is as badly bitten as you are saying, your family members are probably being bitten, as well. Not a good thing.