If you want to efficiently level up your WoW warrior in the MMORPG Wrath of the Lich King you should definitely resort to a guide. The latest guides are even available as addons for the game, so that you don't have to look things up on a website all the time or to turn the pages of a book.
A good guide will tell you to make good use of the new starting areas of Northrend since the quests available there will turn grey once you hit the new maximum level 80 and thus give only very little gold. At the same time, the quest experience points do not vary noteworthy which is why there is no advantage to be gained for leveling in higher zones as early as possible. On the contrary, the quests in the lower level areas are much easier to accomplish which means that you will get them done much quicker. That way you can finish even the higher levels in approximately 3-4 hours.

When questing in Northrend you should start in the Howling Fjord as alliance and in the Borean Tundra as horde. When finished, you should first switch to the other area you haven't done yet to get to the Dragonblight eventually. That way it is guaranteed that you will accomplish all lower level quests as long as they still yield experience points. And additionally, you can really do all the Dragonblight quests which you would not be able to do when going there prematurely. After that you proceed through the Grizzly Hills to Zul Drak which, in most cases, is already sufficient to reach level 80. That way three entire areas remain to be explored and will yield a lot of gold when you do them at level 80.