One of the most effective flea and tick remedies is simply a bath with normal soap and shampoo, which kills most fleas and washes away ticks that have not bitten yet. This should be followed up with a thorough grooming and inspection using a flea comb to find and remove any survivors.
Using warm water and a natural shampoo increases the bath's safety and efficacy. A small amount of dish soap is also a safe and effective cleanser. Citrus-scented soaps may have additional flea and tick repelling properties. Peppermint, lemongrass, rosemary and thyme also tend to repel insects, so using a shampoo with those scents or adding their essential oils to the bath water can help.
Ticks that have already bitten the dog generally need to be manually removed. This is done by using tweezers to grasp the tick as close as possible to the dog's skin without pinching the dog, and then pulling back in a straight line. Commercial tick-removing tools can simplify the process and help prevent parts of the tick from being left in the skin, which can cause infection.
Prevention is probably the best way to handle fleas and ticks in a safe, natural way. Rose geranium oil can be put on a dog's collar before outings to repel fleas, although this should never be used around cats. Covering the dog with an old t-shirt or clothing made for dogs can help keep ticks off its skin.