I agree with dogmother86, puppies under 12 weeks old are too young for topical flea products. A shampoo for puppies or Johnson's tearless baby shampoo and a flea comb are best.
To get rid of fleas on your dog (over 12 weeks old):
Ask your vet for "Capstar" to kill adult fleas, and also use "advantage", "advantix" or "frontline" which only kill immature fleas. That should rid your dog of all fleas. The problem is that you might now have some in your house, so your dog can easily be re-infected. Wash all bedding (preferrably in hot water) and use an anti-flea spray for the home (or anti-flea powder that you vacuum up) to get rid of any fleas that might be on your sofas, rugs, etc. that you can't easily wash. If your dog still has one or two fleas (which I highly doubt if you did all of the above), use a "flea comb" to get them out and drown them in a container of vinegar.
Hope that helps! (It got rid of ALL fleas on my dog! With NO re-infestation for over a month. Remember, you have to reapply "advanitx" or whatever to keep new fleas from hatching on your dog.)