Once you receive a quest, it will be entered into your WoW Quest Log. To access the Quest Log press the default 'L' key. A dialogue window will then appear with complete information on all of your current quests.
The Quests are ordered first by geographic region, and then by quest color and finally by name. A grey color means the quest is likely too easy for you. Green means that there is some danger, but you should be able to handle it. Yellow means there is significant danger involved and you could very easily die, but also that it is possible if you are careful, well-equipped and/or grouped. Red is definitely not advisable unless grouped. "Elite" means you'll need a group or they'll eat you for lunch. As you gain levels, current quests may change color to reflect their new difficulty.
Information in the WoW Quest Log Detailed information including a count of all the quest items you currently have in inventory and other pertinent information such as your objective and reward upon completion.
To abandon a quest, simply bring up the Quest Log (L), find the appropriate quest, and hit the "abandon quest" button at the bottom left. The quest will disappear and the initial quest giver NPC will again have a yellow exclamation point above their head, ready for you to talk to if you wish. In other words, you can still re-acquire abandoned quests.
There is a limit of 25 Quests that you cam hold in your Quest Log. Once you reached that limit you must abandon a quest to add another new quest to your Quest Log. It is advisable to always have 1-2 slots open new quests. Sometimes when you go into an instance and haev to get a questvery quickly, but you do not have an empty slot..... you may not be able to get the quest again until the NPC resets or until you enter a new instance. This situation can hamper your progress.
Due to the limit set in WoW Quest Log, it is wise to try to complete all the quests in one area before moving on to the next one. Do not be afraid to abandon quests and go back to do them later, as you go along, you will learn how to manage your quests better, and obtain several quests involving the same monsters or region before doing them.
Your quest log will usually include the character that you are to return to along with the quest description. When you find the appropriate NPC and have all the required quest items (if any), you will receive xp but you may have the chance to choose between a number of items. If this is the case, highlight the item and click the "complete quest" button at the bottom. In other cases, the reward may be set and you just have to click the "complete quest" button at the bottom of the dialogue window.
Use the WoW Quest Log often and you'll have no worries.