In order to solve an artifact you need to collect between 25 to 100 fragments. These fragments do not take up bag space. The amount you need to collect seems to be random with each artifact. To see how many you need, click the Archaeology skill button. Then select the race icon that is highlighted. Keep in mind that several race icons can be highlighted at one time, back you may be accustomed bits from altered races. You just charge to bang on the one you are alive on at that moment.
Once you have collected the required amount of fragments, you can solve an artifact. All you have to do is click the solve button on the Archaeology screen (See image below.) The antiquity will again arise in your bag. Save it. Any balance bits you accept will be activated to your next project.
The types of fragments you find is dependent on your level in Archaeology and the region that your are surveying.
Dwarf, Fossil, and Troll: Found in Eastern Kingdoms
Night Elf: Found in Kalimdor
Draenei and Orc: Found in Outland
Nerubian and Vrykul: Northrend
Tol’vir: Found in Cataclysm zones
Occasionally, you will find keystones that are for specific types of artifacts. These keystones may be inserted into teh keystone slot in the Archaeology screen and count for 12 fragments. The antique will afresh appear in your bag. Save it. Any antithesis $.25 you acquire will be activated to your next project.