When you start off in the world of warcraft you might notice a whole load of yellow !'s over heads of NCP's, these mean that they have a quest for you, quests are a great way of getting xp and money, and even in some situation rare items! When you accept the quest a silver ? hangs over the head meaning you need to complete it. Quests normally follow the pattern of kill and retrieve, collecting, slaying and talking to other NCP's. When you have done a quest the ! turns into a yellow ? meaning that you can return the quest
After you have mastered the basic rules of WoW you will start traveling out and exploring places within your level range, instances will be introduced, in these you will have to work as a team at healing, damage and tanking to defeat the monster and bosses inside, the bosses drop money and very nice items. The quests for instances give you very nice rewards of items, gold and experience.
You can enter battleground at the level of 10 although i don't recommend it at that level as the bands are 10-19, 20-29, 30-29... so you will be fighting people 9 levels higher then you and it wont be very fun for you, but when you have reached a level that you feel good about entering the arena you have to remember that these are not NCP so they will be more powerful and in some cases, most skillful then the NCP's that you come across.
The art of making money in WoW can be very simple or very hard depending on what server you chose, on some servers the market is very large and cheap, but in others it might be smaller and more expensive so be aware of this when you choose you methods and professions. You are given a wide range of professions to choose from so choose the ones that you think will help you, but will also give you the opportunity to earn money from, one thing you should be aware of though is that enchanting is an expensive profession, but very rewarding, i recommend that you don't take this up for your first character.
When you have developed your style of playing the game and met new friends you should slowly master the game in your own way, the above are just a few things to get you started in Azeroth. Have fun!