Tamriel's Fighters Guide has no presence in Skyrim. Instead, warriors seeking adventure and kinship may join the Companions in Whiterun.
The Companions act as the warriors guild of Skyrim, which is similar to the Fighters Guild. The Companions he no real leader but he a Harbinger named Kodlak Whitemane who also acts as their leader. When asking Torvar who is in charge, he will tell you that no one is in charge of anyone, as they are only in charge of themselves. The Companions reside in a building called Jorrvaskr, which is the oldest building in Whiterun.
First Encounters
You will first encounter Aela the Huntress, Farkas, and Ria at the Pelagia Farm outside Whiterun, they will be seen fighting a Giant. You can choose to assist them in this fight and they will react positively to you, if you don't, Aela will criticize you. Otherwise, Aela will invite you to Jorrvaskr. You may completely miss this encounter if you trel to Whiterun from a different route. Since the Companions are able to defeat the giant quickly, it might be hard to attempt to assist. Shooting an arrow from afar will still count if you don't think you can reach the giant to perform melee attacks in time, the Companions will remain and Aela will speak to you.
Joining The Companions
Whether you are invited to Jorrvaskr or not, simply heading there and speaking to the members until they tell you to speak with Kodlak Whitemane will be enough. Vilkas will not be welcoming of you in the beginning but still follows Kodlak's requests to train you. During this sparring session with Vilkas, you are only allowed to use melee weapons that are not enchanted or your bare fists. Vilkas will surrender and ask you to run an errand to Eorlund Gray-Mane, the blacksmith at the skyforge. There will be a long list of errands you will need to complete for the members so once you've completed this, a radiant quest will be assigned to you as your initiation to The Companions.
Ceremony of The Circle
The senior members of The Companions are also members of The Circle, which makes them Werewolves. There is also a known group of werewolf hunters called the Silver Hand. In an early Companions Quest, Proving Honor, where you witness Farkas transforming into a werewolf. You may become a werewolf as well if you complete a few more quests and speak to Skjor, he and Aela will offer Lycanthropy to you. A special ceremony will commence if you agree to he the ability to transform into a werewolf.