Archaeology Guide 1-525

This Archaeology Guide is updated for the most recent patch and Cataclysm.
Archaeology is the newest WoW secondary skill, set to be released with Cataclysm. Here are some of the very basics of it:

Digsites
Once you train Archaeology you will then be able to see digsites on your map (big map - not your little mini-map). There are four digsites per continent, which will only change once you dig one out. So this means that there will be four digsites for the Eastern Kingdoms, four for Kalimdor, four in Outland, and four in Northrend (once you are high enough level). You find the digsites in zones of your level or lower, so a level 20 won't find digsites in places like Northrend yet because they are too low of a level. But on the other hand, a level 83 will find them anywhere.
Also, interestingly, digsites are player-specific, which means you won't have other player competition like you would with something like herbalism, running for the same herb.
Also, all sites are race specific, meaning you'll only find fragments of one race per site. The race that you will be discovering fragments of is also pretty obvious at times (like Dwarf ruins in the Eastern Kingdoms).

Fragments
You'll be able to search each digsite three times at which point it will disappear and you will have a new digsite to search. So, you could technically ignore one digsite if you didn't want to go to its location because once you clear one of the other three you'll always have a new one to search and you won't be limited or run out and be forced to dig in a spot, that's assuming you don't not want to go to all four!
In order to search a digsite you will need to use your "Survey" skill. This tool will spawn and basically point you in the direction a fragment. Red indicates you are far away, yellow means you are closer, and green means you are within about 40 yards of the fragment.
Once you find the fragment you will receive a fragment that is specific to a race...which brings us to....

Artifacts
Once you get this fragment for a race you'll be able to start a research project. You can work at one artifact per race only but when you have enough fragments you can solve that artifact. You can work on one of these projects/artifacts per each race. After completing an artifact you will be rewarded with something as valuable as the skill it took to get. So for example, at lower levels you will get common items but at higher more difficult levels and artifacts that require a lot of fragments will offer better rewards.
The rarer the artifact the better the item you will get. You can get blue/purple items and some are basically worthless in that they aren't usable but some are weapons and armor which are account bound and can be passed around to your other characters.

Leveling Archaeology

Leveling Archaeology to 525 is pretty straight forward but will take a long time. Keep in mind some of this information may change when Cataclysm goes live. It was last updated during the Cataclysm beta.

Levels 1-100
To start off, head to your faction's Archaeology trainer in either Stormwind or Orgrimmar. You will need to be level 20 to get started.
Archaeology Leveling Trainer
Now you've gained two abilities, Survey and Archaeology. For the first 100 levels we'll only use Survey and avoid Archaeology. Let's start by heading to our first digsite. To find one, open up your map and look for shovel icons.
Archaeology Digsites Map
Once you arrive at a digsite, use your Survey ability and your character will survey the site and determine the location and distance the artifact is away from your current location. The scope will point in the direction of the artifact and the color of the light will tell you if it's very close (green), near by (yellow) or far away (red).
Survey Digsite Far Away
Notice as you get closer, the color changes to green:
Survey Digsite Very Close
Once you find and receive the artifact you will gain one level. You can survey each digsite 3 times and you will always have 4 digsites available per continent. Continue surveying until level 100. Try to avoid completing artifacts until you've reached level 100 since you will no longer be able to level by surveying after level 100.

Levels 100-525
Once you're level 100, you're done leveling by finding artifacts (although you'll need finding artifacts). Now you should complete your artifacts by solving them. You can do this by using your Archaeology ability and selecting 'Solve' where you have enough artifacts to do so. This will give you 5 levels per completed artifact as well as a novelty item, often worth a few silver or gold to a vendor. As you reach higher levels and solve better artifacts there are novelty items, Bind on Equip and even Bind on Account items available from Archaeology.