At the Military Buildings you can start the timed process of recruiting and training fighting units. You can select how many units to train at a time, increasing the amount of populace, time, and silver needed.

When you start the game only one military building is available to you. Which one depends on your race. New buildings become available as you level up and complete research.

Elf Dwarf Human
Scout Camp (Scout) Infantry Post (Maceman) Soldier's Hall (Soldier)
Skirmish Camp (Skirmisher) Command Post (Infantry) Cadet Academy (Cadet)
Archery Range (Archer) Bunker (Riflewoman) Target Range (Slinger)
Quarters (Guard) Forge (Axeman) Soldier's Hall (Soldier)
Sacred Grove (Healer) Aid Station (Curer) Field Hospital (Medic)
Acrobat Pillar (Acrobat) Siege Tower (Grenadier) Guard Tower (Swordsman)
Stockade (Crossbowman) Forward Base (Trapper) Castle (Knight)
Warrior Den (Elite) Armory (Crusher) Stables (Cavalry)
Sorcerer's Sanctum (Conjurer) Garrison (Shieldman) Mystic Lair (Enchantress)
Monastery (Cleric) Arena (Berserker) Grand Church (Priest)
Den of Shadows (Assassin) Guardian Dome (Guardian) Barracks (Halberdier)
Longbow Legion (Sharpshooter) Steamworks (Flame Thrower) Sanctuary (Paladin)
Wizard's Tower (Wizard) Fort (Cannoneer) Dragon Trainer (Dragon Rider)
Gold Sentry Camp (Sentry) Gold Launcher Station (Launcher) Gold Javelineer Tent (Javelineer)
Gold Warrior Lodge (Warrior) Gold Bishop Chapel (Bishop) Gold Barbarian Fort (Barbarian)

For more detailed info on each race's buildings: