Skyrim Walkthrough: Companions Quests - Take Up Arms

If you want to start the Companions questline, which lets you become a Werewolf, follow this walkthrough. The first thing you want to do is to join the Companions Guild. You get introduced to the companions near Whiterun, so you might already have the quest in your quest journal, under Miscellaneous. It will say, "Speak with the leader of the Companions" If so, you can skip the next steps and go straight to Jorrvaskr in Whiterun.

Approach Pelagia Farm, near Whiterun, to the south. You witness a few warriors fight a Giant. Watch as they defeat him. After the fight, Aela the Huntress will approach you, telling you it's all taken care of but no thanks to you. If you say you tried your best she will ridicule you and call you a "Milk Drinker". Glory awaits only those who triumphs, and as companions, their glory must always be hard fought. If you say they didn't look like they needed help, she will say that certainly not, but a true warrior always stands up to challenge a giant. She will say that's why she is here, with her shield brothers - The Companions.

Ask Aela who are the Companions. She will realize you are an outsider, because you have never heard of the Companions. The companions are an Order of Warriors. Brothers and Sisters in honor. And they show up to solve problems if the coin is good enough. Ask her if you can join them. She will say it is not for her to say, and that you need to talk to Kodlak Whitemane  in Jorrvaskr if it's in you to join the Companions.

To reach Jorrvaskr, enter Whiterun, Go east to the market, then take the stairs to the north towards Dragonsreach, but instead of continuing north, climb the stairs to the east towards the big house with the shields. That is Jorrvaskr.

Inside Jorrvaskr, watch Athis and Njada brawling. Head towards the south of the house, and down the stairs, into the Jorravvskr living quarters. Then to the North. Kodlak will be in the room talking to Vilkas. Vilkas will say he still hears the call of blood. Kodlak will say that they all do, it is their burden to bear, but they will overcome.

Talk to Kodlak Whitemane. Tell him you would like to join the Companions. He will say he sees the spirit in you, but Kodlak will protest about having an unknown outsider join. Kodlak will say that what matters is your heart and arm.

Kodlak will ask how are you in battle. Tell him you can handle yourself. He will tell you that Vilkas will test your arm.

Open your quest journal:
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.

Objectives:
Train with Vilkas

Follow Vilkas outside. He will tell you to have a few swings at him so he can see your form. Draw your favorite melee weapon and strike at him. He will block your attacks with his shield. He will say not bad, next time it won't be so easy. He will give you his sword and tell you to take it to Eorlund to have it sharpened. Your objective now is to give Vilka's sword to Eorlund. Climb up the steps and find Eorlund Gray-Mane standing near a forge. Tell him that Vilkas sent you with his sword. He will ask you if you are the newcomer. Ask him if Vilkas always sends newcomers on errands. He will tell you not to worry about it, they were all whelps once themselves. Ask him if he also is a Companion. He will say that no, but they don't know how to use the forge so he serves them. He will tell you that there is noone really in charge of the Companions, although Kodlak is sort of an Advisor.

Tell him you need to be going. He will ask you a favor. He has been working on a shield for Aela and wants you to deliver it to her. Agree, and your task now is to bring Aela her shield. Take the shield and go back into Jorrvaskr. Locate Aela, probably in the living quarters downstairs. Tell her you have her shield. She will remember you from the giant encounter. She is talking to Skjor who says he saw you training with Vilkas. She asks you if you think you could handle Vilkas in a real fight. Tell her you don't care for boasting.

She will ask Farkas to show you to your room. Follow Farkas to your quarters.  He will tell you to go to him or Aela if you are looking for work, and once you have made a name for yourself, Skjor and Vilkas will have some things for you to do. He will welcome you to the companions.

This completes the quest "Take up Arms". At this stage, Farkas will ask for your help in some matter, this is a minor quest you need to complete, such as "Trouble in Skyrim" in which a group of bandits has been causing trouble in Whiterun, and you need to kill the leader of Silent Moons Camp. Once you help him (or another Companion) with his task, you will unlock the next quest, "Proving Honor".