Duke Hydraxis, a quest giver
Quests are the core of the World of Warcraft experience. From around level 10, you will almost always have a dozen active quests in your quest log. A lot of the time, if you're like many, your log will have the maximum of 25 quests in your log. It is good, however, to limit this as well as is reasonable, because others frequently have quests to share with you. The more of the group working on the same quest, the better, as you can all work to a common goal and you each know distinctly what that goal is.
Quests are obtained from NPCs, from items in the world, or shared from party members. Not all quests can be shared, and there are many quest lines that you must follow from the beginning; you cannot skip within a quest line. Along with the Lua error in package.lua at line 80: module 'Module:Inlinegfx/img_link_data.json' not found. expansion, NPCs who offer quests will have their names floating above their head (green for quest givers of the same faction and yellow for quest givers who will give quests to either faction or are not yet friendly.
In your starting area, you will find some quests that are common to all, and for some classes, you will have some class-specific quests. All of these quests are good to start gaining experience. These often include killing low-level creatures in the area or speaking to one of the nearby NPCs.
interact with quest giver 
quest giver out of range
You can identify quest giving NPCs from the ! over his head. Talk to the quest giving NPC to get the quest. The giver of a quest you have yet to complete will have above his head a silver ?. When you complete the quest by meeting its requirements, the quest giver will have a ? over its head. These symbols will also appear on your mini-map to help in navigation and discovering new quests.
- Note: If you have the requirements, but some items are in the bank, you must retrieve them to finish the quest. They must be in hand. Otherwise, it will appear as though the quest is bugged when it's not.
Most of your first 10 levels will come from quests and from monsters you kill as a part of doing quests. While a good group is a very good thing, if you find yourself in a party that wanders around killing non-quest monsters and doesn't seem to be working towards a quest, it may be better to go questing alone. Most frequently, groups involving different classes are much more effective than groups of only one class, or being solo. Also, in groups, players can share many quests with one another so that all of them can be doing the very same quest, and if the quest involves only killing monsters, each monster killed contributes to everyone's quest. If a quest involves picking up an item from one specific mob, all party members can pick it up at once.
You should always take the time to read the quest information. It will almost always tell you where to go in order to complete the quest objective, or occasionally tell you to check an item in your Inventory for detailed information regarding your objectives (quests that do not tell you where to go or what to do are few and far between).