* Diggerest 100 common artifacts will take a while -- you'll almost certainly have maxed archaeology by the time you do it. On the plus side, you don't really have to make any especial effort for this achievement, because you'll be putting tons of common artifacts together on the hunt for the rares and epics.
* I Had It in My Hand The first of three Indiana Jones quotes now used as achievements. You'll only have to put a single rare artifact together for this one, and this will usually happen around 150-200 skill (perhaps less if you're putting artifacts together as early as possible rather than just leveling by digging to 100). I still think that Blizzard missed a WOW Gold clear chance at some fun with a potential "Adjunct Professor" title, with NPCs programmed to /spit as you walked by.
* What was Briefly Yours is Now Mine If you're fantastically lucky, you may get this with blue-quality artifacts before you even max archaeology, but I wouldn't count on it. Otherwise, there's just a little luck and a lot of work involved.
* It Belongs in a Museum! If I recall correctly, this was actually rewarded for putting together all of the rare artifacts on the beta, not 20 rares/epics. There are 26 rare/epic artifacts currently available, so you'll still have to put together almost all of them to get this -- and you'll also have to be at least 450 to pull it off, as that's the earliest that you can make the epic BoA artifacts. (It's for that reason that players recommend not solving any artifacts for a race from which you want/need an epic until you reach 450 from other races.)
There are seven civilizations and a set of fossils to be discovered, so eight types of artifacts total. Brief descriptions and a few notes on each are below:
* Draenei Draenei artifacts can only be found in Outland. In my opinion, they get the best and coolest rare artifact in the game, the Last Relic of Runescape Money Argus, which can teleport you to one of 20 random places in Azeroth or Outland. Too bad about the lengthy cooldown, but I think it's fun as hell.