With some references, and pictures courtesy of this site
And with links courtesy of MMO-Champion

There's a video available at the end of this post.

Thanks to all my guildies in <Zion> of Duskwood, for their never ending support. This started as a post I made for them (and for me!) to just have a 1-stop reference of where all the Rares could be obtained - and after endless whispers asking for more information, it quickly blew-up into what you see below! Hope it can be of as much use to others as it's been to me and my friends!

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Glossary of Terms

Fragment: The items collected directly from digsites which appear in the progress bar(s) of your Archaeology window

Keystone: The green items which are also collected from digsites & will be kept in your bags; are used in the sockets available during a Solve. Can be traded among players & sold/bought on the Auction House. Each Keystone is equivalent to 12 Fragments when doing a Solve.
The Keystones:
Dwarf Rune Stone (Dwarf)
Highborne Scroll (Night Elf)
Troll Tablet (Troll)
Fossil - no keystone
Draenei Tome (Draenei - Outland)
Orc Blood Text (Orc - Outland)
Nerubian Obelisk (Nerubian - Northrend)
Vrykul Rune Stick (Vrykul - Northrend)
Tol'vir Hieroglyphic (Tol'vir - Uldum)

Artifact: The Common (grey) or Rare (blue or purple) items which you earn from combining the Fragments & Keystones

Solve: The act of combining Fragments/Keystones into Artifacts (rare or common)

Survey: The ability you use to locate Fragments & Keystones in a digsite

Digsite: The locations on your map where you use your Survey ability to find Fragments & Keystones

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Where Can I Train?

Doktor Professor Ironpants - Ironforge (Hall Of Explorers)
Harrison Jones - Stormwind (Royal Library)
Hammon the Jaded - Darnassus (Temple of the Moon)
Diya - Exodar (Vault of Lights)
Dariness the Learned - Dalaran (The Legermain Lounge)
Boduro the Seeker - Shattrath City (Lower City)

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How do I Survey?

Once you've trained, open your map and you'll see shovels scattered around each continent.

VERY IMPORTANT: Survey will only grant skill-ups until skill 100. After that, you will NOT get anymore skill-ups from gathering fragments. After 100 skill, you can only get skill-ups from Solving Artifacts (described later).
It is strongly recommended to NOT do ANY Solve combines until AFTER you have reached 100 skill in Archaeology.

Here's an example of digsites around Eastern Kingdoms, identified by the shovel icon on your main map:


When you zoom-in on the zone, this is what your survey area will look like. Digsites do not appear on your minimap in any way:


Once you've trained, your professions window will look something like this:


You have 2 tools available: Survey, and Archaeology. Survey is your new "gathering" ability; Archaeology is your "tracking" window. Fly to a digsite, click Survey, and you'll see one of the following appear on the ground beside you:


** THE TELESCOPE POINTS YOU IN THE DIRECTION YOU NEED TO TRAVEL **
Red could mean flying to the opposite side of the digsite; green could mean taking only a few steps forward.

The items you collect are called fragments, and look like one of the following depending on the digsite type:

Kalimdor & Eastern Kingdoms:


Outland:


Northrend:


Uldum (Tol'Vir fragments are *ONLY* available in Uldum):


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Where can I use it?

There are specific skill requirements for each continent; you won't see the digsites until you have reached the appropriate skill.

At any given time, there will only be 4 digsites active on any continent.

So at skill 375, you'd have 4 digsites in Kalimdor; 4 digsites in Eastern Kingdoms; 4 digsites in Outland; and 4 digsites in Northrend.

Once you're high enough level to Survey in Cataclysm zones, they're considered part of their associated continent. So any digsites that appear in Uldum will be out of the 4 available in Kalimdor; any digsites that appear in Twilight Highlands will be out of the 4 available in Eastern Kingdoms, and so on.

Skill Required // Area
1 // Eastern Kingdoms, Kalimdor
300 // Outland
375 // Northrend
450 // Cataclysm

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How can I get the Goodies?

When you click the Archaeology ability, it will open to a page that looks something like this:


You can go back to the above window by clicking the blue flag at the top right of the Archaeology window ("Current Artifacts").

Clicking on each race will show a window similar to these:



The orange bar at the bottom shows your fragment collection progress. Once the bar is full, you can click the "Solve" button & will get the item displayed at the top of that window.

Some items will have a socket appear, where you can insert keystones. Keystones are collected from digsites using Survey, and will remain in your bags until you use them.

There can be anywhere from 0 to 3 sockets, and each Keystone converts into 12 fragments when socketed.

An example of a socketable item:


Any additional fragments/keystones above the number required to Solve will overflow into the next Artifact.

Clicking the purple tab on the Archaeology window ("Completed Artifacts") will show all the Rare & Common Artifacts you have collected, as shown here:


** IMPORTANT **
From the Blue Post on Archaeology:
You will never get a rare artifact more than once
So if there is a specific Rare you're trying to collect, you'll know it HAS to be your next Rare for that race once you've collected all the other possible rares!
For example, I have all the Dwarf rares (listed below) except the staff - so when the RNG is in my favor and my next Dwarf solve is a Rare, it can only be the Staff.

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Where Will I find Fragments for Each Race?









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What are the Rare Goodies?

Fossil:
Fossilized Hatchling
Fossilized Raptor

Dwarf:
Clockwork Gnome
The Innkeeper's Daughter
Chalice of the Mountain Kings
Staff of Sorcerer-Thane Thaurissan

Night Elf:
Highborne Soul Mirror
Druid and Priest Statue Set
Queen Azshara's Dressing Gown
Bones of Transformation
Tyrande's Favorite Doll
Kaldorei Wind Chimes
Wisp Amulet

Troll:
Zin'rokh, Destroyer of Worlds

Draenei:
The Last Relic of Argus
Arrival of the Naaru

Orc:
Headdress of the First Shaman

Nerubian:
Blessing of the Old God
Puzzle Box of Yogg-Saron

Vrykul:
Nifflevar Bearded Axe

Tol'Vir:
Crawling Claw
Scepter of Azj'Aqir
Staff of Ammunae
Pendant of the Scarab Storm
Ring of the Boy Emperor
Scimitar of the Sirocco
Canopic Jar which has a chance to contain Recipe: Vial of the Sands (recipe only visible if you are an Alchemist). Recipe is BoP, crafted "mount" is BoE.

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There Are Archaeology Quests? Zomg!

Yes. Quests. These are all dailies. Each turn-in awards around 25g, and a group-wide buff:

Each daily can only be completed by one person in the group, and the buff is group-wide. There is no duration, and it persists through death/wipes, but ONLY works inside the instance where the daily was obtained. It was able to be picked-up by an Archaeologist with 460 skill. Stands to reason that once you're at 450 & can use Archaeology in the Cataclysm zones, that these quests become available.

Blackrock Caverns:
Dark Iron Contingency Plan
Requires 1xDwarf Rune Stone (Dwarf Keystone) to complete
Buffs group with Dark Iron Contingency Plan

Halls of Origination:
Map of the Architects
Requires 1xTol'vir Hieroglyphic (Tol'vir Keystone) to complete
Buffs group with Map of the Architects

Stonecore:
Might of the Earthen
Requires 1xDwarf Rune Stone (Dwarf Keystone) to complete
Buffs group with Might of the Earthen

Lost City of the Tol'vir:
Tol'vir Heiroglyphics
Requires 1xTol'vir Hieroglyphic (Tol'vir Keystone) to complete
Buffs group with Tol'vir Secrets

Grim Batol:
Vengeance of the Wildhammer
Requires 1xDwarf Rune Stone (Dwarf Keystone) to complete
Buffs group with Vengeance of the Wildhammer

Throne of the Tides:
Waters of Elune
Requires 1xHighborne Scroll (Night Elf Keystone) to complete
Buffs group with Waters of Elune

The Vortex Pinnacle:
Whispers of the Djinn
Requires 1xTol'vir Hieroglyphic (Tol'vir Keystone) to complete
Buffs group with Whisper of the Djinn

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What Achievements are Available?

All achievements award 10 points each

It's Always in the Last Place You Look - Collect an artifact from each race

Skill:
Journeyman in Archaeology - Obtain 150 skill
Expert in Archaeology - Obtain 225 skill
Artisan in Archaeology - Obtain 300 skill
Master in Archaeology - Obtain 375 skill
Grand Master in Archaeology - Obtain 450 skill
Illustrious Grand Master in Archaeology - Obtain 525 skill

# of Common artifacts combined:
Digger - 10 common artifacts
Diggerer - 50 common artifacts
Diggerest - 100 common artifacts

# of Rare artifacts combined:
I Had It in My Hand - 1 rare artifact - Title: Assistant Professor
What was Briefly Yours is Now Mine - 10 rare artifacts - Title: Associate Professor
It Belongs in a Museum! - 20 rare artifacts - Title: Professor

Common Artifact Collections:
Blue Streak - Dwarf collection
Scorched Staff of Shadow Priest Anund
Dented Shield of Horuz Killcrow
Notched Sword of Tunadil the Redeemer
Silver Kris of Korl

Kings Under the Mountain - Dwarf collection
Moltenfist's Jeweled Goblet
Ironstar's Petrified Shield
Winged Helm of Corehammer
Mithril Chain of Angerforge
Skull Staff of Shadowforge
Warmaul of Burningeye
Spiked Gauntlets of Anvilrage

Seven Scepters - Various Races
Atal'ai Scepter - Troll
Scepter of Bronzebeard - Dwarf
Scepter of Charlga Razorflank - Dwarf
Scepter of the Nathrezim - Draenei
Scepter of Nekros Skullcrusher - Orc
Scepter of Nezar'Azret - Nerubian
Scepter of Xavius - Night Elf

The Boy Who Would be King - Tol'vir collection
Cat Statue with Emerald Eyes
Soapstone Scarab Necklace
Tiny Oasis Mosaic
Engraved Scimitar Hilt (in-game Achievement says "Pommel", actual item is "Hilt")
Sketch of a Desert Palace
Canopic Jar

The Harder they Fall - Orc collection
Tiny Bronze Scorpion
Gray Candle Stub
Rusted Steak Knife
Maul of Stone Guard Mur'og

Tragedy in Three Acts - Night Elf collection
Cloak Clasp with Antlers
Hairpin of Silver and Malachite
Delicate Music Box
Chest of Tiny Glass Animals
Cracked Crystal Vial
Silver Scroll Case