What's the best way to kill fleas?

Time to call in the professionals and consult the vet. Have the house professionally fumigated, and the yard treated as well. In the meantime, visit with the vet about the best products for your area. In some places, some products were more prescribed than others, and the fleas in the area may have developed a resistance to them. So while Advantage may not have worked, another product like Revolution, Advantix, or Frontline may work better for you. There are also oral monthly products like Sentinel, and oral products that can be used in conjunction with topical products, such as Capstar, in order to quickly kill any fleas on the dog- the topical products can take a little while to work.