Upon entering the main building of the Khans' camp and talking to Garl Death-Hand, the leader of the Khans, the Vault Dweller must tell him that they want to join, and "kick some serious ass" (choosing any other dialogue option will only make the Khans attack them). Garl will then proceed to tell the player character that he is tired of his female slaves, and that the Vault Dweller must prove themself by killing the slaves.
Doing so is easy, as they cannot fight back but will simply run away. However, the Vault Dweller must kill them before they leave the camp, as killing them outside the camp will cause the Khans to turn hostile. Once they are killed, Garl will name the Vault Dweller a "friend of the Khans" and grant them free access to the camp.