The bow is one of the main components of the game - When you join, your tribe spawns with one archer minion wielding a bow. Bows are ranged weapons used to shoot both rabbits and enemy minions. An upgrade exists that affects all archers called the shock arrow. This increases the damage outpu of each arrow shot by your minions. Shock arrow also increases the speed in which your arrows fly.
You get a bow using wood. Depending on the number of minions in your tribe, the bow costs 0-5 wood, indicated on the left side of the screen by 0-5 brown little boxes next to the image of a bow. To purchase one, simply grab it with your cursor and drag it to the unarmed minion you want.
Mechanics
Minions with bows will fire once they have locked onto their target. they can be in motion, or stationary, but either way it takes a second or two to load and drawback.
Once they fire, an arrow will be released. Arrows are fairly slow without the shock arrow technology. However, with an arrow, speed doesn't really matter. Bows have a set miss rate, so arrows will not always hit their target.
A minion with a bow will need to be close to its target to lock onto it. This is not a problem in combat, because your two groups will be attracted to each other. It is fairly troublesome when it comes to rabbits. Bow minions will shoot at rabbits only when you bring them close enough. If rabbits hop away, your minions may lose interest.
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An atlantean minion with their bow drawn back
A bow minion
Minions using a bow are not able to be equipped with a shield. However, currently(as of early January 2018) you are able to equip a shield first, and then a bow. Whether this is a glitch or not hasn't been confirmed by the developer.
Tips and Tricks
Minions with bows are the last attacked in a fight if there are other minions for the enemy to attack first. As such, they will usually get away from a fight alive if you decide to run. They can be valuable in combat, because they will not focus one on one with someone, instead of attacking a minion that maybe one of your other minions attack.
They still, however, may not be the best for combat with large groups because of their slow drawback time and the chance that their arrows will miss.
Food is fairly easy to get, (looting other players, especially with cannibalism, mushrooms, Chests are a few examples; and corn in castle mode) so many players will kill off their archers in favor of better combat, or better resource gathering.
Stay close to rabbits to shoot them, and consider getting the invention Shock Arrow so that you one-shot rabbits.