Whew, I don't miss the days of flea baths and spraying the house. I keep my dog on Heartgard and Frontline year round. There is a pill that will kill the fleas on the dog very quickly. Shelters use it on incoming/outgoing dogs. (I don't know about cats; that can be different) Fleas have a hard shell because their skeleton is on the outside of their bodies. Borax breaks that down and they die.
I would consult your vet about something you can use right now for the dog and that will prevent them coming back. If your yard is full of fleas, you need something you can give on a regular basis.
There are things that are relatively non-toxic that you can use in the yard to keep the fleas down but I am not familiar with what they are.
For the house, I would either get an exterminator or invest in the flea bombs that will kill the fleas AND THE EGGS. You don't want to be doing this every time you turn around.
Good luck. It is not a pleasant problem to have.