The 2 original Battlegrounds, Alterac Valley and Warsong Gulch as well as Arathi Basin have reputations. Alterac Valley is the easiest of the 3 to gain reputation in, since you gain reputation for destroying towers, kills, turning in stuff, winning etc etc. In the other two, you will only gain reputation for completeing certain things such as capping the flag and getting a certain "tick" of resourses.
Getting your reputation up with all 3 Battlegrounds will not be an easy task. It will be very time consuming and will take months (expecially with Warsong Gulch). Besides trying your hardest and doing it with premades, there isn't much you can do to speed up the process.
Battleground Reputation - Alterac Valley
Alterac Valley is by far the easiest of the 3 to gain reputation in. You will gain reputation with etheir the Frostwolf Howlers or Stormpike Army by doing the following things:
Killing an enemy NPC
Destroying a Tower
Turning in Armor Scraps
Turning in Blood/Crystals
The easiest way by far to gain reputation in Alterac Valley is by following the front line around and looting as many bodies as possible. Once you get a a stack or two of Armor Scraps and Blood/Crystals use the medallion to return to town and turn everything in. It won't take long for you to get Exalted, plus you'll get some kick ass honor while you do it.
Battleground Reputation - Warsong Gulch
In Warsong Gulch the ONLY two ways you can gain reputation are by capturing the flag and winning. Since these are the only two ways to earn reputation in this battleground, it will take FOREVER. This is by far the hardest battleground to grind out of the 3. Luckily by giving it a time limit Blizzard made it much easier to grind reputation with the Warsong Gulch factions, however it will still take forever,
The only way to speed up your reputation gain is to find a group of friends and just run WSG all the time. Have fun and most of all good luck.
Battleground Reputation - Arathi Basin
Arathi Basin is the second easiest Battleground to gain reputation in. Here you will get reputation every 200 resources collected. Someone did the math and it will require 720,000 resources collected. So, as with Warsong Gulch you will be here quite awhile. Luckily you won't be here forever. =D
The easiest way you can help your team in Arathi Basin is by guarding a base. Plus guarding a base will help guaruntee that you get more resources which will intern help with your reputation grind. Good Luck!