Beginning of the Warriors Guild quests.
In Whiterun, beside the square (with the Talos statue) that leads to Dragonreach stairs, is Jorrvaskr, home to the Companions. It looks like a big hut and has its own forge and training grounds. Inside this building you will find Kodlak Whitemane, Harbringer of the Companions. Ask him about joining the faction and he will send you on training with Vilkas. Afterwards you will meet the blacksmith Eorlund Greymane which will inquire you to complete errands for him, notably bring a shield to Aela. When done with mundane activities, Farkas will take you to your room.