Finding the Companions
You can find the Companions on the eastern side of Whiterun, south of Dragonsreach. It was built on top of a small hill and looks like it has a boat upside-down as a roof:
You will need to enter Jorrvaskr and turn right straight away. Find the stairs leading below in the direction you are facing. Go through the door at the bottom of the stairs. Turn right again after the loading screen and go all the way to the back of the hall that you are in. You will find Kodlak Whitemane and Vilkas sitting at a table. You will need to talk to Kodlak to join the companions.
Take Up Arms
In this first quest Vilkas will lead you outside behind Jorrvaskr. After he asks you to do so attack him until he tells you to stop. Quest done.
Full Walk Through YouTube Video
Next Quest: Hired Muscle