So you want to be like Brann Bronzebeard? Want to find ancient treasures? Want to ride around on an AWESOME BONE RAPTOR???!?!? Then Archeology is the secondary profession for you!
Sense of direction
1) Train the archeology skill at your friendly, neighborhood archeologist
2) Open up your world map. To see the digsites you must be zoomed in/out to a whole continent (Kalimdor, Eastern Kingdoms etc.). Make sure you have [ ]Show Digsites checked in your map
3) The digsites will be marked with a tiny shovel
4) If you click on the zone map, you can see the actual area of the digsite
5) Now you are able to begin excavating! Head on out to the digsite of your choice, don't forget your hardhat!*
6) Press "P" to open up your spellbook and click on the Proffesion tab. I like to have both the Survey skill and the Archeology book placed on my actionbar for easy access. The Survey tool is what you will be using out in the field.
7) When you first use the Survey tool, a telescope with a colored light will appear. The color of the light represents how close you are to the artifact.
Red - Far away
Yellow - Somewhat close
Blinking Green - Take 10 steps and dig again, almost there!
8) The telescope will point you in what direction to go in
This telescope is telling me to head way back in the opposite direction.
9) After surveying a few times something will pop up!
This is the artifact you have searched for! Once you loot it it will appear in your archeology book in your professions tab under the race.
What do I do now?
After gathering a few artifacts, open up your Archeology book and there will be a list of races. When you are starting out there will only be 4 races; Troll, Dwarf, Night Elf, and Fossils. Click on the race you have been collecting. Lets say you've been gathering Dwarf artifacts. Under the dwarf page there is a brief history of the chosen race. Also there is an item at the very top with its name in big yellow letters and under it, it says the race and the item quality. When you first start out most of the items will be common, but as you progress you will discover even more epic treasures! At the bottom of the page it has a progress bar saying the amount of artifacts you've found out of the amount you need. Lets say the first thing under Dwarf is "Old Crusty Smelly Dwarf Beard" (Hopefully this isn't an actual item). It requires you to find 30 artifacts. Each artifact at a beginning level usually gives around 3-5. Eventually you will have reached the 30 needed and you are ready to solve. Solving an artifact gives you five points each. After solving your first artifact the number needed will go up.
Things to Remember:
There are only three artifacts to be found in one dig zone and after that you have to move on, but there is an unlimited amount of "Survey" you can use in a dig site.
Getting your skill up will take a while and requires you to travel around the world
If you want to continue digging but have lost steam, try taking a break for a few dungeons or battlegrounds.
Archeology is like a Archery Target, there are different rings and the center is your target (or in this case your artifact!)
A very crude representation of the Archeology Bulls Eye. Please note that the red range is larger than the yellow and green zones.
If you discover one type of artifact that is not the only artifact you will ever find. It depends on which zone you are in.
Further information (Please note, I take absolutely zero credit for this, Simca made the graph and Wowpeadia made the digsite list):