Players level up mostly by questing. In Wrath of the Lich King you will get achievements when you have accomplished all the quest in a zone. Wrath of the Lich King improved and evolved quests beyond what the original WoW and The Burning Crusade offered.
There are still plenty of "kill 10 foozles" quests, Blizzard made a huge effort to offer lots of other quest types. It now pays to actually read the quest texts, because not only has the storytelling improved, but also quite often you need to follow more detailed instructions than just going somewhere and killing something. Another improvement to storytelling is that quest series now often can actually be done one quest after another, without a too steep increase in difficulty forcing you to stop and level up before you can do the end. The quests in one quest hub are also better related to each other, both from a point of weaving a coherent atmosphere, and from the practical point of several quests sending you in the same direction. There are still a lot of quests where you need to go back to the quest giver, only to be sent to the same quest location again for the next step, but the quest givers are usually relatively close in those cases.
Quests in WotLK have also evolved into being better integrated into reputation and crafting. Dungeons aren't related to a specific faction any more, so you don't grind reputation by doing a dungeon repeatedly any more. At level 80 you can gain reputation by dungeon runs, but the faction you are working for will be determined by the tabard you wear, not by which dungeon you visit. For factions that don't have a tabard, quests are the *only* way to increase faction. For tradeskills, specifically for cooking and jewelcrafting (not sure about the others), there are now daily quests which award tokens which you can spend on learning new recipes. Much better than having to hope for a 1% drop chance from some boss mob in some dungeon.