As soon as you have a bow you can design a unit with a bow, just go into the unit designer from the empire screen. The same applies for any other weapon or equipment.
To train multiples of a group you need to unlock them. Logistics is the first and allows you to recruit parties of units (4). To recruit a party, on the training window for a city you have two rows of icons at the top, the one on the left is size and the one on the right is experience (unlocked with research into training). As you unlock further buttons will become available.
Check the tech descriptions and you'll see the ones you need to unlock the various group / experience options. Though note costs and training time increase.
Also, for those who haven't realised yet - any NPC in friendly territory can buy their own equipment from those you have unlocked (you can even purchase mounts without having the relevant resource from the market), just look for the market button on their actions (looks like a pile of gold). Giving them some weapons and armour is generally a good idea if they're going to get into a fight 