Bowmen are trained at Training Grounds that are Level 3 or higher. They are the second unit in the game that you will be able to make and are also one of the cheapest units in the game, although they do cost one Laborer per bowman just as Fighters do.
In battles, Bowmen can deal a huge amount of damage if the enemies do not have a way to reach past the first row and kill them, because Bowmen are 2nd row units, which means that they will only be attacked by units that can reach to the 2nd row, or after all the first row units are dead. More on unit combat can be found in Zechnophobe's Combat Tutorial
|Training Ground||Fighter · Bowman|
|Barracks||Swordsman · Archer · Hoplite · Gladiator|
|Stable||Cavalry · Knight|
|Workshop||Helepolis · Catapult|
|Trading Post||Ox Wagon|
All unit stats by level can be viewed at the Official Help Database