The Frostborn is an Alliance faction that was added in the WoTLK. There are two ways to raise this reputation. One is to complete all of the quests for the faction and do the single daily available to you. The daily that you are able to do for the faction is called "Pushed Too Far".
This daily awards 250 reputation every time you do it. I doesn't take that long to do, however maxing the faction WILL take long to do. So I'm sure you're now asking how long will it take to max your Frostborn reputation. Well here is a rough estimate using a bit of math of how long it will take you to max your Frostborn faction.
Friendly - Honored (24 days)
Honored - Revered (48 days)
Revered - Exalted (84 days)
24 + 48 + 84 = 156 days.
Additional Note: As of patch 3.3 you will gain The Frostborn Reputation in all Northrend Heroics. The amount of reputation you gain is minimal and will not display unless you have reached exalted reputation with the Alliance Vanguard and The Silver Covenant.
Pushed Too Far
You can accept the quest from Fjorlin Frostbrow after completing a long quest chain. When you start the quest you will mount up onto a Stormcrest Eagle. You'll want to fly northeast to the Foot Steppes and look for Stormpeak Wyrms. You can find the Wyrms perched on rocks or flying around in the air. Since they fly faster then your bird the ones you'll want to focus on are the stationary ones.
Your eagle has 3 attacks, Swoop, Eye Gouge and Storm Bolt. You'll usually want to open up with a Storm Bolt then follow that with a Eye Gouge or Swoop. You will be required to kill 16 Stormpeak Wyrms. If you would prefer to not use the Eagle provided you will still recieve credit for killing the wyrms while you're not mounted on the eagle.