How did Slughorn's information on horcruxes actually help Voldemort?

Question

It's no secret that Horace Slughorn gave Voldemort information on making horcruxes, and a major thrust in the sixth book is Harry and Dumbledore trying to find out what Slughorn told him.

With that said, it seems like Voldemort already had a fair bit of information about horcruxes when he went to Slughorn. I'm slightly confused as to how the information Slughorn gave him actually helped him - it's not like Slughorn gave him an article on "how to make a Horcrux in 10 easy steps," and the majority of the things they discussed he already knew. And Slughorn never really answered Voldemort's question about how many horcruxes it's possible to make. That being said, how did Slughorn's information actually help Voldemort, and how was it enough information for him to actually make one?

Answer 1

Ron wondered this too, in Harry Potter and the Deathly Hallows:

"This is the one that gives explicit instructions on how to make a Horcrux. Secrets of the Darkest Art - it's a horrible book, really awful, full of evil magic. I wonder when Dumbledore removed it from the library... If he didn't do it until he became headmaster, I bet Voldemort got all the instruction he needed from here."
"Why did he need to ask Slughorn how to make a Horcrux, then, if he'd already read that?" asked Ron.
"He only approached Slughorn to find out what would happen if you split your soul into seven," said Harry. "Dumbledore was sure Riddle already knew how to make a Horcrux by the time he asked Slughorn about them. I think you're right, Hermione, that could easily have been where he got the information."
_{Harry Potter and the Deathly Hallows, chapter 6}

Answer 2

Mithrandir's answer already provides one relevant quote, but I'd say it lacks interpretation. What helped Tom Riddle was not so much what Slughorn said, but the two things he did not say:

• Something like "no way, splitting a soul a second time leaves too little intact, it would destroy all soul pieces", possibly backed up by the story of someone mad enough to try and fail, would probably have stopped Tom from creating more than one Horcrux. Thus in hindsight Slughorn feels he made Voldemort more powerful by not preventing the creation of multiple Horcruxes instead of just one (which was bad enough).
• And he did not say anything about Tom's rather disturbing question to anyone else. Had he been more suspicious, Riddle could have been stopped before he actually "became" Voldemort. Though I'm not sure he hadn't already created his diary by then.

So in a way Slughorn helped Voldemort by not not helping him.

Answer 3

With thanks to @Mithrandir for his excellent answer and reference, as well as the discussion in the comments on his answer: it didn't help Voldemort in the least. Voldemort already knew how to make a horcrux - he wanted to know if he could make seven of them, and Slughorn apparently either didn't know or didn't care to share.

Given how ashamed he was of his memory of the discussion (as evinced by the fact that Harry had to manipulate him into giving him the information), Slughorn apparently believed he had given Voldemort significant information (or, at least, that he had missed the fact that his "theoretical discussion" with Voldemort wasn't so theoretical after all and that he had failed to take action), but the fact remains that his information wasn't what enabled Voldemort to make horcruxes.

It's unclear exactly how Voldemort found out that splitting his soul seven times would work. Possibly he worked it out himself somehow (or found it in a different book), and possibly he just chanced it and tried splitting his soul multiple times. Or, possibly, as pointed out in another answer, the fact that Slughorn objected that that would be a terrible thing to do (rather than an impossible thing to do) may have been enough to suggest to Voldemort that it was at least theoretically possible.