How do golden retrievers hunt?

They hunt both upland game and waterfowl.

Waterfowl are hunted primarily by watching where the birds have fallen and swimming out and retrieving them. The sense of smell is not used that much.

Upland game is hunted by scent. The dog will run back and forth in front of the hunter looking for the scent of a bird, either, picking up its scent over the air or tracking it on the ground. After shooting the bird the dog will run out and retrieve the bird or if it is a cripple chase it down and retrieve it.

The Golden Retriever's nose is exceptionally strong and one of the things that make this a great hunting dog.

See the question are Golden Retrievers hunting dogs?