The Old Man is a vanilla NPC, found at the steps of the Dungeon as soon as you get there. After beating the Eye of Cthulhu, he offers the Skeletron quest.
Start: Talk to the Old Man
The Old Man talks about how, while he can't remember much, he knows two things: terrible stuff is happening under him, and that he had talked to a man - short, bearded - in a nearby town some time somewhat recently. That's the only lead he gives.
Next: Talk to Thrain Ironfist
Thrain recalls a man in a red outfit passing by. He mentioned a few things while he was there:
He also recalls that the red man said something about “evil powder on a book”, though he's not entirely sure what that meant.
Throwing a vile or vicious powder on a book tile will turn it into Ancient Evil Book
Next: Return to the Old Man and show him 1 Ancient Evil Book, 2 Candles/Platinum Candles, and 1 Demonite/Crimtane Bar
Possessed by the curse that binds him, yet strikingly clear, the Old Man recites two poems:
A light at each side;
One bar of evil below,
A book sits, starting.
Many skulls screaming,
On the bricks of the prison.
A portal appears.
The Ancient Evil Book also has a diagram mimicking this poem in case the player forgets.
Both describe the ritual which would open a portal to the domain of Skeletron, which looks like this:
Next: Enter Skeletron's domain
Skeletron's domain is large and trecherous. Unlike others, the player must explore the dungeon in its entirety, crawling with traps, spikes and other dangers, in order to progress to the dwelling place of Skeletron itself.
There are three floors - each floor having one more room than the last. Each room must be completed in order to progress.
For example, this is a room in the domain:
Each room has a series of obstacles, some much more complex than others, ending in a lever. All levers must be flipped on before continuing.
Next: Kill Skeletron
Next: Return to the Clothier
The Clothier mentions how just a few moments ago, he turned from the Old Man back to his usual self. He thanks you, and says he has things to think about. The quest ends.
The Old Man's dialogue has been modified to fit the new boss domain system, and that you cannot summon Skeletron in the main world.
During the Day:
“...I...don't have anything to say.”
"..."
“The day is long.”
Night, before beating the Eye of Cthulhu:
"You...do you know of a curse...?"
"Hm...I don't...know..."
"Please, don't wait."
“Take caution, friend...”
Night, after beating the Eye of Cthulhu:
“You just might be strong enough...”
“Do...can you? I think you...may...”
“What was it...book...candle...”
“The Dungeon awaits.”
Upon starting:
"Ah...hm? Oh...an adventurer! Hello. I...I don't know who or where I am. But I do know that something terrible is happening, deep below me. I...I can scarcely remember a thing. I do know...a man, shorter, bearded...helped me...some time in the past. In a nearby town. I...don't remember the name. Perhaps look for him? I can't say much else...I'm afraid."
Upon being shown the materials:
"...
A light at each side;
One bar of evil below,
A book sits, starting.
Many skulls screaming,
On the bricks of the prison.
A portal appears..
..."
As the Clothier, after defeating Skeletron:
"It was just a few moments ago I returned to my former self! Wow! Felt like I was miles away from myself, yet here all the same. Well. That marks a moment in time for me. Thank you ever so much for freeing me. I'll...reconsider my choices in profession. I owe you much."