D2 is aquired through a fairly lengthy, somewhat difficult and expensive quest chain through which you upgrade D1 pieces.
Important Note:
During the first run of this content back in 2006 when completing the final quests of each stage where you would turn in your D1 item
for the equivalent D2, if you had multiple items of the same D1 piece (EG, two Bracers), you would lose all of them when turning in the
quest if they were equipped or in your bags. As of writing this we don't know if it will behave this way in WoW Classic,
once we find out I'll update/remove this section but until then just to be safe put any extras in the bank or you may lose them!
Deliana and Mokvar
Depending on your faction you'll be speaking to one of the two NPCs mentioned below quite frequently throughout this chain.
Deliana for Alliance, located in the Great Forge (Throne room) in Ironforge.
Mokvar for Horde, located in the Valley of Wisdom (Warchiefs room) in Orgrimmar.
Part 1: Wrists.
The D2 quest chain starts off very easy.

What you'll need for this stage: Gold: 20

Quests:

[ 1 ]: Alliance: An Earnest Proposition.

[ 1 ]: Horde: An Earnest Proposition.
Alliance: Deliana sends you to Winterspring to collect 15x Winterspring Blood Sample from any frostsaber or bear within the zone.
Horde: Mokvar sends you to Silithus to collect 15x Silithus Venom Sample from any spider or scorpion within the zone.
Once you've collected the samples, return them your factions quest giver along with 20 and you'll recieve the D2 wrists.
Part 2: Belt and Gloves.
Things start getting difficult and expensive from here on.
What you'll need for this stage:
Gold: 80
1x Delicate Arcanite Converter.
4x Greater Eternal Essence.
10x Stonescale Oil.
25x Volcanic Ash. (Quest item, cannot be pre-gathered).

Goblin Rocket Fuel - You'll be given 8 of these from one of the quests and you'll likely need need extras.

Quests: This part begins with faction specific quests.

[ 1 ]: Alliance: A Supernatural Device.
[ 1 ]: Horde: A Supernatural Device.
[ 2 ]: The Ectoplasmic Distiller.
Mux Manascrambler asks you bring him the following materials needed to create the Ectoplasmic Distiller along with 40.
1x Delicate Arcanite Converter.
4x Greater Eternal Essence.
10x Stonescale Oil.
You'll also be sent to collect 25x Volcanic Ash, which can be collected in Burning Steppes. There's no specific area, you'll find it everywhere within the zone.
[ 3 ]: Hunting for Ectoplasm.
For this you'll need to use the Ectoplasmic Distiller, which drops a physical object on the ground and consumes 1x Goblin Rocket Fuel, close to the undead mobs mentioned above. You must stay within 20 yards of the device (you will have the Ectoplasmic Distiller buff reapplied every 3 seconds while in range) and the undead mob must also die within 20 yards of the device. If you or the mob are outside this range when it dies you won't be able to loot the ectoplasm. The device itself will last 5 minutes before despawning and you'll need to resummon it.Best way to do this is place the distiller close to the center of each area and pull mobs into its range, kiting if required. You will likely need extra fuel for all 36 ectoplasms.

Once you've collected all required return to Mux Manascrambler and hand in.

[ 4 ]: A Portable Power Source.
Mux Manascrambler sends you out to collect a Magma Core from Magma Lord Bokk in Burning Steppes.
Hes a non-elite and very easy to kill. Collect the core and return to Mux Manascrambler.
[ 5 ]: A Shifty Merchant.
Mux Manascrambler sends you out to buy 1x Fel Elemental Rod from Vi'el in Winterspring.
This annoying imp has set-up shop surrounded by level 60+ elites in Darkwhisper Gorge and sells the rod for 40.
Once you've got it, return to Mux.
[ 6 ]: Alliance: Return to Deliana.
[ 6 ]: Horde: Return to Mokvar.
Mux Manascrambler gives you the Extra-Dimensional Ghost Revealer and finally sends you Deliana / Mokvar.
[ 7 ]: Alliance: Just Compensation.
[ 7 ]: Horde: Just Compensation.
Talk to Deliana / Mokvar again and you'll recieve the D2 Gloves and Belt.

Remember to put any duplicates of the of the D1 gear you're exchanging for this stage of the quest series in your bank or you may lose them!

Part 3: Pants, Shoulders and Boots.
What you'll need for this stage:
3x Dark Iron Bar.
3x Mooncloth.
20x Enchanted Leather.
4x Cured Rugged Hide.
8x Large Brilliant Shard.
4x Dark Rune.
Quests:
[ 1 ]: Alliance: In Search of Anthion.
[ 1 ]: Horde: In Search of Anthion.
Deliana / Mokvar sends you off to find and speak to Anthion Harmon who is unfortunately dead. Head over to the Stratholme Main Gate entrance in Eastern Plaguelands and use your Extra-Dimensional Ghost Revealer to see him. You'll find him wandering on the bridge.
[ 2 ]: Dead Man's Plea.
This quest takes place in Undead Stratholme.
Anthion Harmon asks you to save Ysida Harmon from Baron Rivendare. Immediately after opening the second service gate you will have 45 minutes to start fighting Rivendare. You do not need to kill him within 45 minutes however if your timer expires during the fight and you wipe you will immediately fail. This was one of the most challenging parts of this series in its original release, in classics release I've had groups clear under 45 minutes with random pugs, even in phase 1. A guide was created for it, which you can find here, though you probably won't need it.
[ 3 ]: Proof of Life.
Ysida Harmon sends you back to Anthion Harmon with her locket to prove you saved her.
[ 4 ]: Anthion's Strange Request.
Anthion Harmon asks you to bring him the following materials to craft the Incomplete Banner of Provocation.
3x Dark Iron Bar.
20x Enchanted Leather.
3x Mooncloth.
4x Cured Rugged Hide.
[ 5 ]: Anthion's Old Friend.
Anthion Harmon sends you off to find Falrin Treeshaper in the library in Dire Maul North. To access the library you'll need someone with the Crescent Key, which is obtained from Pusillin in Dire Maul East.
[ 6 ]: Falrin's Vendetta.
Falrin Treeshaper asks you to collect 25x Ogre Warbeads from any ogre within Dire Maul or Blackrock Spire. Once you have all 25 return to Falrin.
[ 7 ]: The Instigator's Enchantment.
Falrin Treeshaper asks you to bring him 1x Jeering Spectre's Essence. This drops from Eldreth Phantasm, Eldreth Spectre, Eldreth Spirit or Eldreth Apparition in Dire Maul West.
8x Large Brilliant Shard.
4x Dark Rune.
[ 8 ]: The Challenge.
Falrin Treeshaper gives you the finished Banner of Provocation and asks you to retrieve the Top Piece of Lord Valthalak's Amulet, which is held by Theldren in Blackrock Depths.
[ 9 ]: Alliance: Anthion's Parting Words.
[ 9 ]: Horde: Anthion's Parting Words.
Return to Deliana / Mokvar and you'll be rewarded with the D2 Boots, Pants and Shoulders.
Part 4: Helm and Chest.
What you'll need for this stage:
Gold: 120 to buy Hallowed Brazier. You'll also need honored with the Argent Dawn.
1x Flask of Supreme Power.
You'll also need the materials and friendly reputation with Cenarion Circle to summon The Duke of Cynders.
1x Twilight Trappings Set - These are a common drop from any of the Twilight Cultist mobs in Silithus.
1x Twilight Cultist Robe.
1x Twilight Cultist Mantle.
1x Twilight Cultist Cowl.
1x Twilight Cultist Medallion of Station.
1x Signet of Beckoning: Fire. - This isnt required but you'll only have a 25% chance to summon The Duke of Cynders without it, meaning you may have to farm all these materials again.
Quests:
[ 1 ]: Alliance: Bodley's Unfortunate Fate.
[ 1 ]: Horde: Bodley's Unfortunate Fate.
Deliana / Mokvar sends you to meet another ghost, Bodley who is sitting directly outside the Blackrock Spire entrance. You'll need to use the Extra-Dimensional Ghost Revealer to see him.
[ 2 ]: Three Kings of Flame.
Bodley asks you to collect the remains of 3 fire elementals.
Incendicite of Incendius - From Lord Incendius in Blackrock Depths.
Ember of Emberseer - From Pyroguard Emberseer in Upper Blackrock Spire, who is the first boss.
Cinder of Cynders - From The Duke of Cynders a world boss in Silithus.
The first two are relatively easy, both from dungeons.
The third is dropped from a world boss. He isn't too difficult, the equivalent of a dungeon boss so bring friends.
To spawn him you must equip the following and talk to one of the three Wind Stones in Silithus.
1x Twilight Cultist Robe.
1x Twilight Cultist Mantle.
1x Twilight Cultist Cowl.
1x Twilight Cultist Medallion of Station.
You will have a 25% chance to spawn him when talking to the wind stone unless you have the Signet of Beckoning: Fire in your bags, in which case you are gaurenteed to get The Duke.
[ 3 ]: The Four Components of Importance.
Bodley will send you off to collect one of the four items below, the quest he offers you is random for each player, even within the same class and faction. While all the mobs you are sent to kill are elites they're fairly easy to solo.
Components of Importance: Starbreeze Village Relic - Frostwhisper Gorge in Winterspring.
Components of Importance: Druidical Remains - Hive'Regal in Silithus.
Components of Importance: Soul Ashes of the Banished - Purgation Isle Hillsbrad Foothills.
Components of Importance: Brilliant Sword of Zealotry - Tyr's Hand in Eastern Plaguelands.

[ 4 ]: The Left Piece of Valthalak's Amulet.
Bodley then asks you to find the Left Piece of Valthalak's Amulet. Like above you'll be given one of the four quests at random.
You can loot the quest item from any of the below bosses even if its not the one you have the quest for (for example if a group member summons it during their quest), however each quest requires you kill the specific boss for your particular quest as part of its objectives so you'll need to do it anyway to be able to turn in.
[ 5 ]: I See Alcaz Island In Your Future...
Bodley sends you to Alcaz Island in Dustwallow Marsh to collect 20x Bloodkelp from the Naga.
Alcaz Island is full of elite mobs and they are very difficult to solo. You will likely need a group (2-3) to complete this. Once done return to Bodley.
[ 6 ]: Four more Components of Importance!
Like before Bodley will send you to collect one of the four items below.
More Components of Importance: Starbreeze Village Relic - Frostwhisper Gorge in Winterspring.
More Components of Importance: Druidical Remains - Hive'Regal in Silithus.
More Components of Importance: Soul Ashes of the Banished - Purgation Isle Hillsbrad Foothills.
More Components of Importance: Brilliant Sword of Zealotry - Tyr's Hand in Eastern Plaguelands.

[ 7 ]: The Right Piece of Valthalak's Amulet.
Exactly like the left piece Bodley will give you one of the four quests below at random to collect the right piece.
The Right Piece of Lord Valthalak's Amulet: Stratholme Live.
You'll need to kill Jarien and Sothos.
These two are summoned using the Brazier of Beckoning in Balnazzars room.
The Right Piece of Lord Valthalak's Amulet: Scholomance.
You need to kill Kormok.
He's summoned using the Brazier of Beckoning in Ras Frostwhispers room.
The Right Piece of Lord Valthalak's Amulet: Lower Blackrock Spire.
You need to kill Mor Grayhoof.
He's summon using Brazier of Beckoning in War Master Voones room.
The Right Piece of Lord Valthalak's Amulet: Dire Maul East.
You need to kill Isalien.
She's summoned using the Brazier of Beckoning in Alzzin the Wildshapers room.
Once complete return to Bodley.
[ 8 ]: Final Preparations.
Bodley asks you to bring him 1x Flask of Supreme Power and collect 40x Blackrock Bracer, these are dropped from any orc in Lower/Upper Blackrock Spire.
[ 9 ]: Mea Culpa, Lord Valthalak.
Bodley will give you the Brazier of Beckoning and sends you to kill Lord Valthalak in Blackrock Spire. He is summoned in the room of The Beast.
This can be a somewhat difficult fight.
Rather than post the strategy here, there are many guides on how to defeat him from the original classic run still available on his wowhead page in the comments section.
[ 10 ]: Return to Bodley.
After Lord Valthalaks death you'll meet the Spirit of Lord Valthalak where he was slain. He sends you back to Bodley. The reward for this quest is the Brazier of Invocation, this is permanent and allows you to summon any of the bosses from this quest chain, even those you did not get a quest for.
[ 11 ]: Alliance: Back to the Beginning.
[ 11 ]: Horde: Back to the Beginning.
Bodley sends you back to talk with Deliana / Mokvar.
[ 12 ]: Alliance: Saving the Best for Last.
[ 12 ]: Horde: Saving the Best for Last.
Show All Class Quests:
Speak with Deliana / Mokvar again and you'll be given your last pieces of D2, the Helm and Chest.

Finally, I would like to add that rogue darkmantle armor, darkmantle gloves, darkmantle boots, darkmantle cap, darkmantle tunnel are highly recommended. (4) Set : Chance on melee attack to restore 35 energy.