"Farewell, Aragog, king of arachnids, whose long and faithful friendship those who knew you won't forget! Though your body will decay, your spirit lingers on in the quiet, web-spun places of your forest home. May your many-eyed descendants ever flourish and your human friends find solace for the loss they have sustained."
-- Horace Slughorn giving Aragog's eulogy
Professor Slughorn sneaks some of Aragog’s venom while Hagrid isn’t looking, then gives a grand eulogy that Hagrid finds very touching.
After Aragog’s body is in the ground, Hagrid and Slughorn bond over drinks.
The bodies of Acromantula are not usually laid to rest; Hagrid removed Aragog’s corpse from the Forbidden Forest before the rest of the Acromantula clan could devour their patriarch’s remains.
Aragog’s health was failing during the summer of 1996.
Hagrid sent a note asking Harry, Ron, and Hermione all to attend the burial. Ron opted to stay away due to his fear of spiders in general and Aragog in particular, Hermione didn’t think it was worth sneaking out of the castle against school rules for, and Harry had planned on staying with the other two until the Felix Felicis made him feel that he should go, after all.
Hagrid was understandably upset: He hatched Aragog and raised Aragog, and had him when he was mostly alone in the world.
We know this happens on April 21 because Apparition tests were the same day, and the sign posted in the Gryffindor common room in HBP21 specified the date. This works well with our calendar, too; the 21st is a Monday, we already know from [HBP9 that Harry has Potions on Mondays, and most of his lessons with Dumbledore have happened on Mondays, as well.
In his letter inviting the trio to pay their respects, Hagrid explains that the burial will occur around dusk because that was Aragog's favorite part of day.
Like Slughorn did at Aragog's funeral, Bill Weasley filled Dobby's grave with a silent wand movement (DH24). It is unclear whether both wizards are adept at nonverbal magic for a more common movement charm or if there is a spell specifically for filling graves. -BB