The information in this article may have been changed over the release of previous expansion packs. I will verify the information and update as needed.
The League of Arathor is the faction you gain reputation with when you compete in the battleground Arathi Basin. The only way to get reputation with this faction is to compete in Arathi Basin battles, and by completing the couple quests that become available to you as you move from Neutral through to Exalted.
The Battle for Arathi Basin! (Alliance, 25) is the first quest you have access to and is availble at the Neutral level. For this quest you will have to assault each of the Mine, Lumber Mill, Blacksmith and Stables. This quest will carry over to other Arathi Basin battles, so you don’t have to worry about assaulting all 4 bases in 1 battle.
The second quest available is Control Four Bases which you gain access to once you reach the Friendly level. For this quest, your team will have to assault and defend 4 bases until the end of the battle.
The third and final quest is titled Control Five Bases and becomes available at the Exalted level. If you guessed you have to assault and capture 5 bases to complete this quest, you are absolutely correct. Once this quest has been completed you will have access to the Arathor Battle Tabard.
Other than completing those 3 quests you get 10 reputation points per 200 resources collected, except on Arathi Basin weekends, when you get 10 reputation points per 150 resources collected. To win a battle your team needs to collect 1600 resources, which means you get 80 reputation per win on a regular day, and roughly 106 rep per win on an Arathi Basin weekend.
Some Math:
Assumptions: Only battling, not completing any quests. Only competing on regular days, not including Arathi Basin weekends. No loses only wins.
Neutral -> Friendly = 3000 Rep = 38 Wins
Friendly -> Honored = 6000 Rep = 75 Wins
Honored -> Revered = 12000 Rep = 150 Wins
Revered -> Exalted = 21000 Rep = 263 Wins
38 + 75 + 150 + 263 = 526 Winning Arathi Basin Battlegrounds to go from Neutral to Exalted.
You will earn the achievement:
Knight of Arathor
You will be on your way to earning the following achievements:
Master of Arathi Basin
The Justicar
Battlemaster
100000 Honorable Kills