The Valiance Expedition reputation is one of 4 reputations added in Wrath of the Lich King in the Alliance Vanguard Sub catagory. This factions main hub is Valiance Keep which is located in Borean Tundra. The Alliance can easily get to Valiance Keep from the boat at the Stormwind Harbor.
There are two ways for players to raise their Valiance Expedition reputation. One way is to complete each of the quests available to you from the Valiance Expedition. The other way is to not wear a faction specific tabard while running Northrend Heroics.
I'd like to also note, to prevent confusion. It will show your Alliance Vanguard faction and your Silver Covenant Faction increasing but not Valiance Expedition faction. If your Alliance Vanguard and Silver Covenant faction is exalted then it will display your Valiance Expedition faction as increasing. However if you're not exalted with Silver Covenant and the Alliance Vanguard, you will still gain Valiance Expedition faction.
It's confusing I know. But you'll understand once you see it happening.