Upon entering the main building of the Khans' camp and talking to Garl Death-Hand, the leader of the Khans, tell him you want to join, and "kick some serious ass" (choosing any other dialogue option will result in the Khans attacking you). Garl will then proceed to tell you that he is tired of his female slaves, and that you must prove yourself by killing them.
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 against him/her. Once they have been killed, Garl will name the Vault Dweller a "friend of the Khans" and grant him free access to the camp.