• You need to have Chief/Senator/Chieftain.
    Then, once the Residence or Palace of your target is destroyed (with catapults), you need to attack the village with one of these units (don't forget to put a few troops with him, you wouldn't want your expensive chief dying :p). It will lower the village's approbation. Once the approbation reaches 0, your chief/Sena/Chieftain dies and you conquer the village.

    Note that you can't conquer a player's capital though.

    The amount of approbation reduced depends on the tribe you're playing (a Senator lowers approbation more than a Chieftain), the population of attacker & defender, and the celebrations.