"The home of Pyromancy, Izalith, was scorched by the very fire it created. Undoubtedly, it was a flame of chaos, tangled by a witch's hand. But who's to say that this Bonfire's flame is any different?"
Cornyx is first found locked inside of a small cage in the Undead Settlement, in a scaffolding of the small fortress found near the guillotine and where three hollows throw firebombs from above.
To reach him, drop from the right side of the bridge nearby and onto a ledge below. Follow the only path available (lighting the Cliff Undersidebonfire along the way), which leads to a piece of roof and the scaffolding of the structure, and eventually to Cornyx's cage. When asked, agree to become his pupil in the arts of pyromancy.
Once he relocates to Firelink Shrine, he can be found in the basement, near to the base of the staircase on the east wing, and reside there for the rest of the game.
"Ah-ha, Unkindled are we? Welcome to my abode. I am Cornyx, an old pyromancer. A crow in his cage as you see, now. But here we are, an encounter for the ages! I hear the Unkindled make for fine vessels. Care to learn pyromancies from this old man?"
"Yes"
"Most wise. A chance encounter should not be squandered. To reiterate, I am Cornyx, of the Great Swamp. The pleasure is mine."
"No"
(snickers) "Most foolish. This old crow has a little knowledge on his own, you know. Bah. No sense in spelling it out. I will not rush you. You will return, once you are enlightened. We are, after all, both Undead. And both prisoners in our own ways." (snickers)
Firelink Shrine
"Ahh, there you are, Unkindled One. I wish to express my gratitude. For trusting a lowly pyromancer, and allowing me to gaze upon this majestic flame. As promised, I will impart pyromancies to you. But first you will need a flame of your own. Careful you don't burn yourself with it."
Talk
"Heed my words, Unkindled One. Fear the fire. The home of pyromancy, Izalith, was scorched by the very fire it created. Undoubtedly, it was a flame of chaos, tangled by a witch's hand. But who's to say that this Bonfire's flame is any different."
Giving him the Carthus Pyromancy Tome
"Well, well...I've never seen anything like this. This inscription...this tome is from the Catacombs. Fascinating. On this day, the teacher learns alongside the pupil." (laughs)
Giving him the Izalith Pyromancy Tome
"Ah, what have we here! A pyromancy tome from Izalith! Then you've found the home of Pyromancy. Brilliant. I will never curse being old and Undead again. Now, now, show it here, quickly. Let us channel them together. The primal pyromanices known only to old Master Salaman!"
Giving him the Quelana Pyromancy Tome
"Ahh, what have we here... By the gods. This inscription reads Quelana, the ancient deity, one of the witches of Izalith... The last of them, who wandered the lands. Then she must have returned to Izalith, after all. But I regret to say, I cannot accept this. Quelana's pyromancies are for witches, and must be learned from a mistress. But thank you, for allowing me to peer upon such a thing. If only I were a woman." (ha!)
Giving him the Grave Warden Pyromancy Tome
"I'm afraid I cannot accept this. This pyromancy tome is dark, and delves into the depths of men, where an untouchable flame resides. I cannot comprehend this myself, let alone teach it to you. It is a spell forbidden in the Great Swamp, and nearly everywhere else, too. Only on terribly afflicted, or burdened by deep sorrow, could begin to understand this."
Attacking
"Why? What's the matter?"
Making him hostile
"Fine, fine, I see how it is. When a pupil strays from the path, the master must intrude."
Killing the player
"Spare the rod and spoil the child."
Death
"I can't complain... This old reverie... had to end..."
Killing him while in his cage
"Little bird, what's to be gained?"
Player leaves
"Do not be gone for long. What's a teacher without a pupil?"
Notes
Teaches the "Welcome" gesture upon talking to him a second time after a loading screen takes place.