They discuss Rufus Scrimgeour and view two memories: in the first, Morfin tells Voldemort about his family just before Voldemort kills the Riddles; in the second (which Slughorn has modified), Voldemort asks Slughorn about horcruxes. Finally, Dumbledore sets Harry homework – to obtain the rest of Slughorn’s memory. (HBP17)
It was upon visiting Morfin that Tom learned that his father was a Muggle. Tom Stupefied Morfin, then went to the Riddle house and murdered his father and grandparents. Before leaving Little Hangleton, Tom stole the ring that was a Gaunt family heirloom.
As a student, Riddle asked Slughorn about Horcruxes. In the version of the memory Slughorn has supplied, things go a bit wonky as Slughorn is observed to scold Riddle for wanting to know about such things.
This happened the first day back from the Christmas holidays, and a "few days after New Year." On the HBP calendar, this is Monday, January 6.
When questioned by the Ministry, Morfin confessed to the murders, so Tom must have also implanted false memories. Morfin died at Azkaban during his second incarceration. (HBP17)