Voldemort is known for his unfading desire to gain immortality. In book 1, Voldemort tried to steal the stone not to gain immortality but he believes that it has the power to bring back his body since he was a 'soul form' at that time.
Indeed, the stone's powers are quite remarkable and can help Voldemort rise to power.
However, how did he know about the stone?
He may have read about it in Hogwarts: A History or possibly A History of Magic (which was required reading for first year students).
Given Tom's independence and thirst for knowledge, it makes sense that he would read as much as possible about his chosen subject, which undoubtably would lead him to the library, and more research.
Plus, he made friends with students with noted relatives in the magical world (The Slug Club), and could have used this to gather more information about magical history.
The Dark Lord could have easily found out that Nicolas Flamel had made a Philosopher’s Stone. The existence of the Philosopher’s Stone, as well as that Nicolas Flamel was the only known maker of it, wasn’t hidden. In fact, it was the achievement he was most famously known for. It was fairly well-known and wasn’t considered ‘restricted’ or ‘dangerous’ like knowledge of Horcruxes - it was in at least one easy-to-get library book, where Hermione finds the information about him.
“There have been many reports of the Philosopher’s Stone over the centuries, but the only Stone currently in existence belongs to Mr Nicolas Flamel, the noted alchemist and opera-lover. Mr Flamel, who celebrated his six hundred and sixty-fifth birthday last year, enjoys a quiet life in Devon with his wife, Perenelle (six hundred and fifty-eight).”
- Harry Potter and the Philosopher's Stone, Chapter 13 (Nicolas Flamel)
The book Hermione had found was one she’d gotten out of the library for a bit of light reading - it wouldn’t have been in the restricted section or otherwise hard to get, she seems to have just picked it out off the shelf. She wasn’t even trying to find information on immortality or Nicolas Flamel when she’d chosen it, it just happened to have a part in it about the Philosopher’s Stone.
“Harry and Ron barely had time to exchange mystified looks before she was dashing back, an enormous old book in her arms.
‘I never thought to look in here!’ she whispered excitedly. ‘I got this out of the library weeks ago for a bit of light reading.”
- Harry Potter and the Philosopher's Stone, Chapter 13 (Nicolas Flamel)
It’s mentioned in this book for sure, and is likely mentioned in others - the Dark Lord could have found out about it from any of them. In addition, he may or may not have even been actively seeking information about immortality when he found out Nicolas Flamel had created the Philosopher’s Stone. He was interested in immortality, so he’d certainly pay attention to anything about it, whether or not he was actually seeking the information at the time he’d found out about it.
Tom Riddle had a good education. He most likely learned about the Stone through a book at Hogwarts. We know that he is in the books there; Hermione finds him there.
As @Alistair86 says, A History of Magic would be a good option, because first years are required to read it. He wouldn't have found out about the Stone in Hogwarts: A History, though, because why would Flamel be in there, unless it was for his work with Dumbledore?
If you're asking how he knew that the Stone was at Hogwarts then Quirrell told him.
