The same reliable source on IMDB has leaked a page from the script about this scene; various shots came from various sources; Bold, Italicized Lines have been seen in either Sneak Peeks or Trailers, and have been changed to reflect them.
HBP Script Leak
How is he? Horace?
Harry shrugs. Dumbledore nods, then tips his hand. A LONG strand hangs suspended like glass. A pearl forms...and as it hangs...
Harry's eyes shift, notice a DRAWING on Dumbledore's desk, one of Tom Riddle's drawings seen at the orphanage, of the CAVE and the distinct OUTCROPPING. Then...
...the pearl drops.
116 INT. SLUGHORN'S OFFICE/YEARS PAST - NIGHT
As before. The CRACKLING EMBERS of the FIRE. Slughorn, a circle of six. Riddle commanding the room.
Sir, is it true that Professor Merrythought is retiring?
Slughorn chuckles, wags a sugar-encrusted finger at Riddle.
Now, Tom, I couldn't tell you if I knew, could I? I must say, m'boy, I'd like to know where you get your information. More knowledgeable than half the staff, you are.
(as the other boys laugh)
By the way, thank you for the pineapple--you're quite right, it is my favourite--how is it you knew?
Riddle smiles but his expression suggests intuition had nothing to do with it. Slughorn chuckles uneasily.
Good gracious, look at the time. Off you go, boys, or Professor Dippett will have us all in
detention. Lestrange, Avery, don't forget your essays...
As the others file out, Slughorn busies himself with some papers when--Ping!--
he turns, finds Riddle still there, standing by the crystal hourglass.
Look sharp, Tom. You don't want to be caught out of bed after hours...
I know a secret shortcut or two.
Yes, I imagine you do. Something on your mind, Tom?
Yes sir. I couldn't think of anyone else to go to. The other Professors, well, they're not
like you. They might...misunderstand.
Riddle slips off the RING on his left hand, begins to roll it between his fingers. It is set with a BLACK STONE.
I was in the library the other night, in the Restricted section, and I read something rather odd, about a bit of rare magic, and I thought perhaps you could illuminate me. It's called, as I understand it...a Horcrux.
Slughorn's weak smile evaporates altogether.
Horcrux. I came across the term while reading and I didn't fully understand it.
I'm not sure what you were reading, Tom, but that's very Dark stuff, very Dark indeed.
Yes sir. Which is why I came to you. I mean no disrespect to the rest of the staff, but I thought if anyone could tell me...it would be you.
Slughorn frowns, clearly disturbed, then speaks quietly.
A horcrux is an object in which a person has concealed part of their soul.
Yes, I thought it might be something like that. But I don't understand how that works, sir.
One splits one's soul and hides part of it in an object. By doing so, you are protected should you be attacked and your body destroyed.
That part of your soul that was hidden, lives on. In other words, you cannot die.
Riddle nods and TURNS AWAY, staring at himself in the MIRROR on the wall opposite. A hint of RED glints in his eyes.
How does one split his soul, sir?
I think you can guess the answer to that, Tom.
Yes. Killing rips the soul apart. It is a violation against nature. After, one is never the same.
Out of curiosity, sir--can you only split your soul once? For instance, isn't seven the most
powerfully magical number--
Seven! Merlin's beard, Tom! Isn't it bad enough to think of killing one person? To rip the soul into seven pieces...
This is all hypothetical, isn't it, Tom? All academic...
Of course, sir. And I promise I'll not speak of our conversation. It'll be our little
Riddle reaches out then and pinches the FLAME of a candle, killing it. As SMOKE RISES, we DISSOLVE into...
117 INT. DUMBLEDORE'S OFFICE - SAME TIME - NIGHT
...the surface of the Pensieve, where Riddle quivers. We RACK FOCUS and Dumbledore's troubled face bleeds through Riddle's.
Dumbledore holds up his withered hand, silencing him, turns away. Harry studies him, waiting, the hush palpable.
(haunted) This is beyond anything I imagined. In my life I’ve seen things that are truly horrific. Now I know you will see worse.
Dumbledore looks off, his eyes distant. Harry watches him intently, as do the HEADMASTERS in their frames above. Finally, tentatively, Harry speaks.
Do you mean to say he succeeded, sir? In making a Horcrux?
Oh he succeeded. And not just once. Think, Harry. He's just told us.
Seven. He made seven--the most powerfully magical number. But...what are they exactly?
They can be anything. The most commonplace of objects. A ring, for example. Or a book...
Dumbledore slides open a drawer, removes the RING and Tom
Riddle's battered DIARY.
Tom Riddle's diary--
It's a Horcrux, yes. Four years ago, when you saved Ginny Weasley's life in the Chamber of Secrets, when you brought me this--
(holding up the diary)
I knew. This is a different kind of magic. Very dark. Very powerful. But until tonight I had no idea just how powerful...
And the ring...?
Belonged to Voldemort's mother. It was difficult to find and...
(raising his damaged
...even more difficult to destroy.
But if you find them all. If you destroy each Horcrux...
One kills Voldemort
Harry begins to reach out for the ring...
But how would you find them? They could be hidden anywhere, couldn't they...
True. But magic, especially Dark magic...
Just then, as the flesh of Harry's fingers make contact with the ring, IMAGES FLASH by in DIZZYING succession: VOLDEMORT'S FACE, twisted in pain.
A DERELICT HOUSE, deep in a haunted clearing. An ANCIENT CUP, gleaming as it tumbles from an old woman's hand. A SNAKE (NAGINI) slithering through damp grass.
Dumbledore slipping the ring onto his finger, recoiling as his skin decays...
Harry's clenched hand SPASMS, RELEASES. The ring skitters across Dumbledore's desk and Harry brings a hand to his chest, a look of bewilderment on his face. Dumbledore watches the ring spin down, then glances at Harry and slowly extends his own hand,
lightly touching the center of Harry's chest with the tips of two ashen fingers, as if reading braille, as if he can somehow "see" into Harry's heart. Trepidation--and recognition--flicker over his face. He looks up, meets Harry's eyes.
(It should be noted the above couple of paragraphs were absent from the test screening.)
It's where you've been going, isn't it, sir? When you leave the school.
Harry's eyes drift once again to the postcard on the desk. Dumbledore withdraws his hand, nodding, still studying Harry oddly, his voice, when it comes, distant.
Yes. I think...perhaps...I may have found another. But this time I cannot hope to destroy it alone.
Harry peers into Dumbledore's eyes. Dumbledore nods.
DUMBLEDORE Once again, I shall ask too much of you, Harry.
118 INT./EXT. GARGOYLE CORRIDOR - LATE DAY
Harry stands at a window, looking out. He brings his fingers to his chest again when...Hermione comes up behind him.
Harry. It's time.
119 INT./EXT. COURTYARD - MOMENTS LATER - LATE DAY
Harry, Hermione and Ron walk.
Hermione, is the Room of Requirement unplottable?
If one wants it to be. Why?
It would explain why I thought Malfoy was leaving the castle when he disappeared off the Map. He was going to the Room of Requirement.
Of course, and that explains the Vanishing Cabinet as well!
A calendar picture of Dumbledore, the ring and the diary emerged.
A test screening viewer discusses Horcruxes in the film.
I honestly don't know if those not familiar with the book will understand the horcruxes. I think they will understand what they do and how they work. But I am not sure if it was clear Harry still needed to kill Voldemort in the end, I think it is just assumed. What I don't think a book reader will understand is the significance in the objects chosen as horcruxes. I think the reason why Voldemort chooses those particular objects is not explained whatsoever. I don't think it was ever even mentioned that the locket was Slytherin's.