During one of his lessons with Dumbledore.
it is one of the 7 horcruxes that are needed by harry to finally destroy voldemort
Sometime after the events of book 5, and before the events of book 6. In other words, during Harry's vacation. about 1996 in says in the book
It was one of Voldemort's Horcruxes, it also has the Resurrection Stone hidden inside it.
It's not destroyed in Fellowship of the Ring. It's destroyed in the Return of the King when Frodo and Sam cast the ring into the fires of Mount Doom.