The Black Temple attunement requires level 70 and starts at The Altar of the Sha'tar for Aldors and the Sanctum of the Sun for Scryers. Both are in Shadowmoon Valley.

Aldor

Aldors start attunement from Anchorite Ceyla at the Altar of Sha'tar in Shadowmoon Valley:
1. Tablets of Baa'ri 
2. Oronu the Elder
3. The Ashtongue Corruptors
4. The Warden's Cage
Scryer

Scyers start attunement from Arcanist Thelis at the Sanctum of Stars:
1. Tablets of Baa'ri
2. Oronu the Elder
3. The Ashtongue Corruptors
4. The Warden's Cage
After that, the chain comes together for Aldor and Scryer.

5. Proof of Allegiance
6. Akama
7. Seer Udalo

Seer Udalo is found in the Arcatraz just before the last boss.

8. A Mysterious Portent
9. The Ata'mal Terrace
10. Akama's Promise
After you finish this chain, you get to pick from some rewards and the chain seems like it ends. It continues however, inside Serpentshrine Cavern from an NPC called Seer Olum who you can speak with after killing Fathom-Lord Karathress. He starts the next part of the Black Temple Chain by offering the quest:

1. The Secret Compromised
For this quest you just return to Akama.
2. Ruse of the Ashtongue
In this quest, you must use the costume Akama provides, and kill A'lar in Tempest Keep: The Eye while wearing the Ashtongue Cowl. Attunement for The Eye is a whole different chain.
3. An Artifact From the Past
In this, you need to gain access to The Battle of Mount Hyjal in Caverns of Time, and slay the first boss, Rage Winterchill. Attunement for this involves killing Lady Vashj and Kael'Thas Sunstrider.
4. The Hostage Soul
For this you must speak with A'dal in Shattrath city.
5. Entry into the Black Temple
Just speak with the naaru Xi'ri in front of Black Temple.
6. A Distraction for Akama
Ensure that Akama and Maiev enter the Black Temple in Shadowmoon Valley after Xi’ri’s forces create a distraction. At the end, you become attuned to enter and are granted The Medallion of Karabor
At this point, you are attuned and can enter Black Temple, although the chain continues and you can soon upgrade your medallion. It continues with:

1. Seek Out the Ashtongue
You just need to find Seer Kanai inside Black Temple.
2. Redemption of the Ashtongue
This involves entering Black Temple, and killing the boss the Shade of Akama.
3. The Fall of the Betrayer
After killing the Shade of Akama and returning to Seer Kanai, he asks one last thing of you. Kill Illidan The Betrayer. After doing so, you are granted the Blessed Medallion of Karabor, an upgraded version of your original medallion, and allows teleportation to the Black Temple.