Available from Level 3.
You need a weapon license to start.
The hunting grounds are located outside the city. The fenced area is marked in red on the map. You can start the job at the hunting lodge.

Starting the Job
Inside the hunting lodge, stand on the job marker and change into your work clothes.

Your work outfit depends on your character's gender.

You'll also receive 50 shotgun shells.
Work Process
Once you start, a marker showing the animal's approximate location will appear on the map.
All job details are shown in the Tasks window.
Head to the marked area and find the animal.

Take out your weapon, aim, and shoot the animal.

You can't damage animals assigned to other players.

Once you've shot the animal, walk up to it. An interaction prompt will appear.

Pick up the carcass.
Take the carcass to the warehouse marked with a red marker.

After you deliver the carcass, the next animal will be marked on the map, and your ammo will be refilled to 100 shells.
Your earnings and the number of animals hunted are shown in the Tasks window.
If you leave the hunting grounds and move far enough away, the job will end automatically. You'll receive your earnings, and the job-issued weapon will be removed.
If you enter a critical state and are taken to the hospital, the job will end and your earnings will be forfeited.
Finishing the Job
To collect your earnings, return to the hunting lodge and end your shift at the same marker where you started.

Wages
You earn 670 units of in-game currency per carcass.