This was originally a long page all about the various flea and tick products... all of which had advantages and disadvantages.
But now (updated March 2020) that the new generation pesticides (isoxazolines) are available, flea and tick control is simple, safe, and very, very effective.
For dogs: I recommend NexGard. It's super safe and super effective for both fleas and ticks... including the ticks that carry Lymes disease for 1 month
Simparica and Bravecto are similar compounds that work well.
Also; Seresto flea and tick collars available online and at pet stores seem to be working well. ( I don't have much experience with these collars in regard to safety or effectiveness)
For cats: I recommend the new, greatly improved Revolution Plus. Revolution Plus now contains sarolander, one of the new generation of pesticides that are super safe and super effective for both fleas and ticks. This is a topical product; you just squeeze a few drops on the back of the next. Revolution Plus also protects your cat from heartworms, intestinal worms, ear mites and mange. And it's even less expensive than the original Revolution.