Take Up Arms The legendary warrior band of Whiterun, the Companions have agreed to let me join them, if I can handle some preliminary tasks for them.
After finishing Speak with the leader of the Companions in Jorrvaskr, Kodlak Whitemane will charge you with your first quest in the order of the Companions: you must engage in some hand-to-hand combat with Vilkas to test your mettle.
Follow Vilkas down the main basement hallway of Jorrvaskr and up to the top floor, then follow up to the eastern doors to go out back. The battle is simple enough: just swipe your weapon(s) at him a few times and it will be over. He'll just hold up his shield the whole time.