Return To Myralion Sunblaze

Here's the entire quest chain, with simple descriptions and quest links for the Horde versions.

1. 
   
2. The Battered Hilt
   Bring the Battered Hilt to Myralion Sunblaze at Quel'Delar's rest, south of the Argent Tournament Grounds.
3. 
   
   2.
4. What The Dragons Know
   Speak to Krasus at the top of Wyrmrest Temple.
5. 
   
   3.
6. The Silver Covenant Scheme (Alliance version is called "The Sunreavers' Plan")
   Obtain the Orders by killing an NPC in the Dalaran Sewers. Make sure you kill the right one.
7. 
   
   4.
8. A Suitable Disguise
   Obtain a Borrowed Tabard from Shandy Glossgleam; He is upstairs in the Threads of Fate: if you are standing in front of the stairs with the Violet Citadel to your back, it is to the right (to the left is the toy store).
9. 
   
   5.
10. An Audience With The Arcanist
    Retrieve the Ancient Dragonforged Blades tome from Arcanist Tybalin. Use the disguise and go in the Alliance section of Dalaran.
11. 
    
    6.
12. Return To Myralion Sunblaze
    Bring the Ancient Dragonforged Blades to Myralion Sunblaze at Quel'Delar's Rest.
13. 
    
    7.
14. Reforging The Sword
    Obtain 5 Infused Saronite Bars and the Forgemaster's Hammer and use them to make the Reforged Quel'Delar. (AKA: Run the Pit of Saron. The infused bars are near the entrance; don't forget you have to kill the boss, too.)(It appears this can be done on Normal Difficulty.)
15. 
    
    8.
16. Tempering The Blade
    Temper the Reforged Quel'Delar in the Crucible of Souls. (AKA: kill the final boss of Forge of Souls; use the quest item nearby.)(It appears this can be done on Normal Difficulty.)
17. 
    
    9.
18. The Halls Of Reflection
    Bring your Tempered Quel'Delar to Sword's Rest inside the Halls of Reflection. (AKA, obviously, run Halls of Reflection.)(It appears this can be done on Normal Difficulty.)
19. 
    
    10.
20. Journey To The Sunwell
    Speak with Halduron Brightwing at the entrance to the Sunwell Plateau on the Isle of Quel'Danas.
21. 
    
    11.
22. Thalorien Dawnseeker
    Visit Thalorien Dawnseeker's Remains and obtain his blessing to wield Quel'Delar. (Go around behind SWP to the Dead Scar (southern end of Isle of QD zone, not in the SWP raid instance) and kill a bunch of mobs.)
23. 
    
    12.
24. The Purification of Quel'Delar
    Immerse your Tempered Quel'Delar in the Sunwell. Speak to a Warden of the Sunwell when you are ready to enter the Sunwell Plateau. (Possibly different versions of this for sword/mace?)
25. 
    
    13.
26. A Victory For The [Sunreavers/Silver Covenant] - (sword or mace)
    Bring the Restored Quel'Delar to the NPC at the Violet Citadel in Dalaran.

A lot of this info came from comments people left on the various quest pages. Thanks to all those who posted useful tips!

This is the conversation that follows after turning in this quest.

Myralion Sunblaze says: The style of this blade and its markings hinted that it might be a dragonforged sword. At last, we will have our answer.
Myralion Sunblaze says: After all these years, can it really be --
Blood-Queen Lana'Thel says: Quel'Delar.
Silver Covenant Sentinel: You are not welcome here, minion of the Lich King!
*Both Silver Covenant guards and Sunreaver guards charge the Blood-Queen, just to be frozen in a block of ice.*
Blood-Queen Lana'Thel says: Quiet, fools. If I had wished to kill you, you'd already be dead.
Blood-Queen Lana'Thel says: As Quel'Serrar was forged by the dragons and given to the Kaldorei, it's twin, Quel'Delar, was given to my people.
Blood-Queen Lana'Thel says: The king bestowed the blade upon my friend, Thalorien Dawnseeker.
*A vision appears of Alexstrasza and two high elves speaking*
Blood-Queen Lana'Thel says: But even Thalorien's skill and Quel'Delar's magic could not save Silvermoon from the might of the Scourge.
Blood-Queen Lana'Thel says: Thalorien fell before the gates of the Sunwell, buying time for others to escape.
*The vision changes to a mounted death knight(Presumably Arthas) killing Thalorien*
Blood-Queen Lana'Thel says: After the battle, I recovered the sword from the field. I bore it to Northrend in the service of my prince, seeking to avenge our people's defeat.
Blood-Queen Lana'Thel says: Arthas shattered our forces and took the most powerful of us into his service as the San'layn.
Blood-Queen Lana'Thel says: My memories of Thalorien went cold and so did his blade.
Blood-Queen Lana'Thel says: It was I who brought Quel'Delar here, to return it to it's makers. In breaking the weapon, so did I break it's power.
Blood-Queen Lana'Thel says: Quel'Delar will never serve another!
*Blood-Queen Lana'Thel destroys the sword and leaves*
Myralion Sunblaze says: It falls to us to see Quel'Delar restored for the Sunreavers.

This quest leads to the follow up Dungeon quests. Starting with:
Reforging The Sword.

It's one of the nice quests in this Chain. After completing the quest Myralion Sunblaze will smash the Sword into the ground and then Lana'thel will spawn and destroy Quel'delar.

EDIT: Uploaded a Screenshot of the conversation.