Extraspecial edit:
http://forums.worldofwar.net/showthread.php?t=381084
Hold your horses ;)
Your rank will be determined by how well you did compared to the other players of your faction. This means how much effort you have to put in can vary a lot from server to server. There is no set number of honor you must achieve to get to the next rank, but you will ofc need to get more and more for every new rank as competition gets harder.
Your rank will also decay. If you stop PvPing altogether your progressbar will go backwards leading to dropping in ranks in the end. This isn't really noticable before you get up to 5-6 as long as you keep it up however (again relative to your server).
It's impossible to tell how much you have to PvP to get to rank 10, but at the end you have to be pretty active to get there. The last few ranks (epic rewards) usually require PvPing pretty much 24/7 over several weeks. Not recomended unless you don't have a job or school.. I'd just start out do what time allows and see where you end up next week (ranks are updated tuesday night).
A lot more things to be said about the honor system, but I'll leave it at that.
As for gaining honor efficiently you should try getting a group together and regularly PvP with them (a "premaid") . Focus Arathi basin and Warsong gulch.
edit: look at honor instead of kills on your PvP tab. How much you get for a kill will vary a lot. Kills are by no means a good way of telling where you'll end up. The honor from winning AB and WSG fast is greater than kills as you will get diminishing returns when killing the same player over and over.