"And now, now, at last. we shall see. Harry, quickly . . ."
-- Dumbledore as he pours the memory into the Pensieve
Just after midnight on the same evening that Aragog is buried, Harry returns to the entrance to Gryffindor Tower to find the Fat Lady asleep. After the burial, under the influence of a fair amount of alcohol and a rush of sad memories, Slughorn had given Harry the memory of him telling Tom Riddle about Horcruxes. The Fat Lady is annoyed that she had been woken up after midnight. She tells Harry that the password changed at midnight and if he doesn’t like that new policy, he can take it up with the Headmaster. Harry responds that he would be happy to do so, except Dumbledore isn’t in the castle. Behind him, Nearly-Headless Nick informs him that in fact Dumbledore arrived back at Hogwarts a short time before. So Harry heads over to the Head’s office with the memory.
There, Harry and Dumbledore use the Pensieve to watch the problematic memory and see Slughorn inadvertently give Tom Riddle the idea for creating multiple Horcruxes.
Timeline Notes
The burial of Aragog happens on April 21, a date based on the real world calendar, which means that Harry's late night visit to Dumbledore's office would happen in the very early hours of April 22.