Currently combat in Stonehearth is mostly automatic. You have limited controls - mainly by activating defensive mode you can enable the villagers to grab whatever tools they have and fight the enemies (in comparison to the default, where the non-combat villagers will simply cower or flee), or using Party Controls to order your warriors around.
Your main combat units are the footmen, who will automatically engage enemies on sight, or if your villagers are being attacked. The radius of protection can sometimes be bugged: eg your villagers may be under attack outside your walls but your footmen do not respond. This can be rectified by activating "defensive mode". Other units such as archers or mages are coming in the future.
Examples of Combat:
(1) Early demonstration of combat from the developer Radiant Entertainment
(2) Zombie horde battle (From an early mod, not current)
(3) Combat scenes compilation (From an early mod, not current)
Examples of Defend Mode activation:
(1) Demonstration in test world by the developer Radiant Entertainment
(2) Defend mode activation in actual gameplay
The future of Stonehearth combat may feature more of RTS (real time strategy) component. The extent of player control is uncertain at this stage, with the aim of finding a balance between having enough control to be enjoyable (and not frustrating) and avoiding excessive micromanagement.
A discussion by players of their vision of the future of Stonehearth combat can be found here: http://discourse.stonehearth.net/t/lets-talk-military/7988