He tells you to kill various animals. Using the bow is recommended but you may use other weapons for a lesser reward. Sneak towards the animal, wait till you get the "you are in firing range" message and shoot it between the eyes. You'll get between 5 to 20 dollar for killing these animals depending on whether or not you used a bow.
Animals to Hunt
Gray Wolf - Found west of Dodge
White Buffalo - Found south of the Ranch
White Wolf - Near the Indian Trader at Piper lake.
Mountain Lion - In the Northern Rockies, southeast of the Indian Hunter.
Great Wolf - Found in the Badlands
Grizzly - Near Empire.