I have been contemplating this over and over again. I have come to several conclusions.
1) That Snape told him, who got the information directly from Voldemort (though it had already gone from the cave, either Voldemort knows it is gone and tried to fool Dumbledore and Snape, or he didn't know it had been moved)

2)Dumbledore found the location on one of his little adventures from school (he must have done alot of research, there are not charmed-style crystals and maps to use)

3)All the remanents from the four founders are inter-related, and can tune into each one's whereabouts (the sword of Godric Gryffindor).

4) Dumbledore is just so awesome that he has some sort of crazy mental psychic ability that can locate anything with significant power.

Yes, the last one was a bit out there but HEY, this is Dumbledore!

Still wondering.......

Great topic!

I think he knew that he had to look for items of significance because of his previous interactions with Riddle as a child. He may have use ligillimens on him then, and known about the cave, or done it on the kids he took there.
Knowing that the event was significant to Riddle made the place significant.

It made sense to look in Gaunt's house, since Riddle had been looking for his roots, and we've known since CoS that Riddle "killed [his] muggle father." DD may also have seen the ring on Riddle's finger, and been able to trace it since it was a relic.

I think it's cool how he can "feel" that places and things are magic. That's something that Harry will need to know to be able to find the rest of the horcruxes.

i think dumbledore found out where to look by he found out important places for voldy. like the cave was a "good important" place to hurt others. it would be cool if dumbledore had this 6th sense kind of thing.

harry needs to learn more still. if he doesnt then he wont accomplish "his mission"

This is a good topic of discussion. It's just as important (maybe more so) to have some idea of where the Horcruxes might be as to know what they are. After all, it's no use wandering around the country looking at all of the old lockets and cups. Dumbledore suspected that Voldemort would stash the Horcruxes in places that had some special significance to him.

So - do we have enough clues from the story so far to guess where they might be? One was in Marvolo's cottage. One was in the cave, and one was in Lucius Malfoy's posession. If Mundungus took the real locket (or perhaps something else) from Grimmauld Place then I suppose Harry will just have to ask him. But what do you think about the old Riddle house? Maybe hidden somewhere at Hogwarts? At the cemetery where Riddle Sr is buried? The orphanage? Or will they be in much more secluded places like the cave?

I think I may come at this topic from a different perspective.

How did Dumbledore know where to find the locket? Simple: Plain and simple detective work. He took what he knew of Riddle/Voldemort, postulated a theory, gathered evidence to support the theory, tested it and proceeded from there...

Of course, we are talking about a very highly skilled wizard, searching for some very powerful magical artefacts, but nonetheless Dumbledore followed the same steps any copper worth his salt would have followed...

Just an opinion...

Cheers!

i think DD knew enough about LV character he could guess where he had hidden them. i think the memories in the pensive are most important to that. The cave, Morfin's hosue. i think (along with Harry) Godric's hollow, the riddle house, his old orphanage. places that hold significance to LV. i guess im just going along with what DD thought

If DD already knew about the horcruxes- collecting all of those memories before Slughorns memory was revealed -why did he need to wait for Slughorns memory? He'd been tracking down people who had been involved with LV and extracting memories way before he even knew for sure that there were even horcruxes.

i think this is a sign of how DD knew about the cave. he has an excpetional mind and amazing memory. he would probably have deduced about the diary, after Harry explained it, and spent long hours deciding about whether LV would have wanted to make horcruxes. after all, being a head must be very boring, as they don't have much to do but watch over everyone.
after this, being DD, he would have taken the risk that it was possible, and maybe searched for people for proof. after he had the memories, he could have been pondering one day and then his first meeting with Riddle could have come to him and he'd have remembered about the woman telling him about the cave. he could have just decided to look for it on the off chance that LV hid a horcrux there, which is where he was going everytime he left Hogwarts in HBP.

of course after the memory, he would have known he was right, and redoubled his efforts at finding the lost cave, because he would have felt almost certain that a horcrux was hidden there. he knew Riddle really well, and knew about the incident in the cave, so as it was a particulalry significant piece of magic, it was clear to DD that LV may have hidden a horcrux in the cave.

(Sorry to bring up an old topic, but I had another thought)

I think it is crazy that Dumbledore somehow is always on the right side of lucky coincidences, it is like he is constantly using Felix Felicis. Think about it....He met Tom when Tom was 11 right?....By then, he had scared the living daylights out of his fellow orphans several times in several different places, so there are several different hiding spots for a horcrux, not to mention other places that are significant to Voldemort. So, it just happens to be that Dumbledore suspects the cave of all places, after probably barely seeing it form an outside glance, and he knows that it is the right one....coincidence, I think NOT.

I am choosing to sick to my earlier argument....

"Dumbledore is just so awesome that he posesses some sort of crazy mental psychic ability to allow him to locate anything with significant power."

Ahh, the possibilities

I don't think Dumbledore was on the right side of a lucky concidence thesolitaryone, I think he went through many possibilities and had lots of places to investigate, but I'd say he had other evidence about the cave that we didn't see. What he told/showed Harry was the most important or compelling piece of the puzzle, not the only one.

Like others said, detective work.

I'd definitely go for the detective work. The memories he obtained from Ogden, Morfin, Winky and Slughorn were necessary to confirm his suspicions, he wouldn't have liked to go by conjecture alone.

so far all of the destroyed horcruxes have been at important places to LV for instance the gaunt house, the cave and hogwarts. so some how Harry is gonna have to find out by his self where LV has either killed an important person or where LV has been over the course of his live.

Harry's got alot to do in 1 book!!

hey i think that dumbledore went around all the places related to voldys past or had any relation with voldy.

I remember Dumbledore voicing an interesting theory to Harry about Nagini possibly being a horcrux but questioned whether or not a living thing could be a horcrux. What if Nagini was an inanimate object when she became a horcrux? Third years are turning teapots into turtles so perhaps an object became a horcrux then was transfigured into a snake to be kept at Voldemorts side so that to get the last one you had to face him. If I were Voldemort that's what I would do.

*Gasp* That is a REALLY good idea! Wow...
Anyway, I never really thought about the possibility of Snape telling Dumbledore where some of the Horcruxes are, although this is likely. However, I didn't think the Death Eaters knew about the Horcruxes. I think I remember Dumbledore saying in Book 6 that the Death Eaters didn't know... ah well.
This is how I think Dumbledore found them (other than Snape's info): Research, research, and more research! I think he actually got out there and started looking. I highly doubt that Dumbledore has some super-human strength to locate all the Horcruxes with a snap of his fingers. I think that Dumbledore learned a lot from the memories he extracted from the people You-Know-Who was related to in some way. After seeing those memories, I think Dumbledore figured it out. I probably would've.

I think that how Dumbldore knew about the Horcruxes was from extracting memories from those that had some affiliation with Tom Riddle/Voldemort. With getting these memories and alot of researching he was able to figure out about the Horcruxes and what they might actually be. But unfortunately he was killed before he and Harry could find out the locations of the remaining Horcruxes and excatly what they were.

I don't know how Dumbledore knew where all the Horcruxes were. I never thought of the possibilities at all that Snape could be telling Dumbledore about the Horcruxes. Voldemort must not have known that Snape was telling him or else Voldemort wouldn't have been very happy about Dumbledore winning. Here is where I don't know where Sanpe stands but this is part of a different topic. I really don't know how but Dumbledore must have been doing stuff with the Horcruxes during his leaves of absent. Snape might have been giving him hints about where they might leave to get Dumbledore out of the school, for what I don't know. I don't think he would want him to getout because of Malfoy and his thing.

Dumbledore didn't know where the horcruxes he disovered where they were by sifting and researching the memories he got and figured the best possible locations. There iz no other way.