How to Join the Companions in Elder Scrolls V: Skyrim
The Companions Quests in Elder Scrolls Skyrim are not part of the main quest, but they are a major faction in the game. The Companions quests offer many missions and there will be many rewards. The Companions are located in the major city called "Whiterun" in Skyrim. Whiterun is marked on your Skyrim map at the very beginning of the game. Whiterun is basically in the center part of Skyrim, a few miles from Riverrun.
How to Join the Companions in Skyrim
To join the companions, you will need to go to a building called "Jorrvaskr." This is in the city of Whiterun at the upper end part, below Dragonsreach. There are a couple of staircases leading up to it, and there is a large tree below the stairs.
Once your inside Jorrvaskr, you will see a couple of new Companion recruits fighting (sparring) with each other. Other companions are watching the fight and offering words to encourage the fight in progress. A man named Skior is over watching the battle. Speak to Skior to gather information on the Companions.
After the sparring is over between Athis and Niada, speak to Niada. She is very rude, but will tell you "Kodlak Whiteman" is in charge. Other Companions will also tell you he is in charge. Once you find out about Kodlak, you can join the Companions.
Speak to Kodlak Whiteman to Join the Companions in Skyrim
Go downstairs to the Jorrvaskr living quarters. Go down the hallway until you find Kodlak Whiteman. He will most likely be speaking to Vilkas. After their conversation, speak to Kodlak about joining the Companions. Kodlak is the Harbinger of Companions (one who is in charge and others pledge their loyalty to).
Vilkas does not seem to approve of you joining, but Kodlak does. You will need to spar with Vilkas, outside in the courtyard to prove your worth. Make sure not to use magic! The Companions do not approve of magic use. Attack Vilkas with one-handed or two-handed weapons.
Elder Scrolls Skyrim - Joining the Companions is great for warrior type characters, especially early on in the game
If you are trying to be a "warrior type character" (one-handed, two-handed, and archery), then joining the Companions will be beneficial early on in the game. Many of the Companions are trainers. You will need gold to get trained. Aela the Huntress, for example, is an expert at archery and can train you.
Also, after completing all of the major quests in the Companions, you can get many of them to be your followers.