You are given the Lordvessel by Gwynevere, Princess of Sunlight in Anor Londo.
In order to get to her, you must defeat Dragonslayer Ornstein and Executioner Smough.
This boss battle is the most difficult you will have faced at this point in the game as it forces you to fight two bosses at once. After one is defeated, the second absorbs his fallen friend's power and is restored to full health for an even more difficult second stage of the encounter.
Provided you met Solaire in the Undead Berg and exhausted his dialogue, he will appear near the bonfire that precedes the Ornstein and Smough fight. Talk to him here and his summon sign will appear in the large room outside the boss fog door on a platform that leads up to a Silver Knight archer. Having Solaire or another human player will make this battle much more manageable.
Note that you need both Ornstein's and Smough's souls for weapons needed for the Knight's Honor achievement, but only the second that is defeated gives their soul. Be sure to alternate the order that you kill them in your two playthroughs.
After defeating the duo, take a lift up and enter the next room where you will find Gwynevere. Interact with her to receive the Lordvessel, unlocking this achievement.
Be sure to interact with her further to discover the Princess's Guard covenant, unlocking the related achievement:
The Lordvessel will allow you to warp between certain bonfires and can be placed at the Firelink Altar to open the way to three of the four main bosses of the game: Seath the Scaleless in the Duke's Archives, Nito in the Tomb of the Giants, and the Bed of Chaos in Lost Izalith.
As always, refer to
http://darksouls.wikidot.com for specific information relating to items or locations.