Your best bet is to get a safe flea killer from the vet. This is a young pup and many people, while well meaning, apply to much flea killer shampoo or when the fleas don't die they repeat the bath. A vet can put a safe and effective flea killer in the right dosage on your pet that will kill the fleas almost immediately.
Over the counter flea shampoo's are not always effective, the collars are not effective either, the drops sold over the counter can wreak havoc with a young pup or any dog if applied wrong. Here are some examples of flea meds gone wrong.
Here are some safer alternitives.
If you choose to use over the counter products then read the directions carefully and go by what the product says. Some shampoos are not safe for pups.