Quest board clearing
The Warchief's Command Board (Horde) and the Hero's Call Board (Alliance) were introduced in Cataclysm as seed quest sources to give players a heads up on what content they might want to do next. At the time it was completely optional and only showed a hand full of quests at any one time. The choices were straight forward anyway and the quest board simply served as a convenient focal point.
These days the quest board is theoretically still optional but it has become both the easiest and most frustrating way to proceed. It's the easiest because changes in game structure have made it more difficult to figure out how to begin the most important quest lines in a specific zone. It has become frustrating because the board was designed to help players based on limited content, the handful of quests mentioned earlier. It now contains over a hundred quests and the content you want can be buried way down deep in the board.
These quest boards need serious redesign to make them more helpful but there are two options you can use to better assist you now. The first is to simply grab quest after quest until you find something you want. Note that the maximum number of quests you can cycle through is 25 and that's only if your quest log is completely clear before you start. You may find what you want or you may not. If not, you'll either have to pick something from the quests you've already accepted or you'll have to go for what's behind curtain #2.
The second option is board clearing. Just grab a few quests off of the quest board and go do them. This isn't a terribly efficient way to play but you do get some experience and coin from this process. There will also be experience from discovering new areas since in many cases this will be the first time these areas are visited. The following two pages contain helpful information for each faction:
Eventually more useful quest lines will be exposed. Some of the better ones are mentioned elsewhere in the hunting lodge.