Depends the class you level. You'll have a tough time if you start off as a warrior, very gear dependent and rather difficult to solo multiple mobs. Druid, Hunter, and Rogue are the easiest classes to level in my opinion. Basically, you'll start off in a small little village, get sent on some quests to fetch x amount of y item, kill x amount of y monster, go to a cave and kill some evil guy, get sent to large city. Around level 10-12 (Horde anyway, not sure on when Alliance gets their first dungeon quests), you'll get sent off with four other people to do some group quests in a dungeon. Kill some difficult monsters, a few bosses, and get some decent equipment.
Here is a pretty well-rounded guide for those new to the game.