How Weapons Work
There are three types of weapons you can equip: hunting rifle, survival bow, and distress pistol.
The bow is the hardest to use but has the added benefit of having the most ammo available because you can craft arrows. The distress pistol is also more difficult to use, but has an added bonus of lots of long-term damage if you actually hit an animal.
Ammo
All ammo is very rare and must be found by scavenging. Rifle ammo can be found in small boxes or in single rounds. Distress pistol ammo is the most rare and typically only found with the pistols. Arrows, however, can be crafted which makes it the most abundant ammo type in the game.
Arrows have a condition and will break when used for a while. Be sure to harvest broken arrows to reclaim the arrowhead and some feathers. All components of arrows can be crafted or forged.
Improving Weapon Skills
You will increase your skill level with weapons the more you use them. Your archery skill will also improve by crafting arrows. The only skill books that exist for weapons are for the rifle.
Other Weapons
If there's a hunting knife, hatchet, or heavy hammer in your inventory it will be automatically equipped and used when fighting off wolves who attack. But these items cannot be equpped like the normal weapons.