Harry, Hermione and Ron exit the Great Hall to visit Hagrid.
Harry and Hermione arrive in the Great Hall and hide inside a closet until they hear their past selves exit, then follow behind them out the door. They go the fastest route to hide in the Forbidden Forest behind Hagrid's Hut.
Harry, Hermione and Ron hide under the Invisibility Cloak and exit the back door as the Minister, Executioner and Dumbledore arrive. They see Buckbeak here, tied in the garden.
Harry and Hermione witness their past selves leaving. They can also see Buckbeak, but do not free him yet because the Minister and Executioner MUST see him.
On the trip back to the castle, Harry, Hermione and Ron hear the thud of an axe and Hagrid's sobs. They assume Buckbeak has now been killed.
Harry and Hermione have successfully escaped with Buckbeak into the Forbidden Forest. Walden MacNair (Executioner), puts his axe into the fence and Hagrid sobs uncontrollably over Buckbeak's narrow escape from death. They now wait in the forest. (Note that the thud of an axe and Hagrid's sobs DID occur, they were only misinterpreted by Harry, Hermione and Ron)
Ron is attacked by Snuffles (Sirius Black), and is dragged under the Whomping Willow into the passage that leads to the Shrieking Shack.
Harry and Hermione arrive at the Shrieking Shack to find Ron with a broken leg and begin a mistaken attack against Sirius Black. They are shortly followed by Professor Remus Lupin.
Professor Severus Snape picks up the left-behind Invisibility Cloak, puts it on and enters the path beneath the Whomping Willow.
After Hagrid leaves his hut, Harry and Hermione take refuge inside it to wait.
Severus Snape arrives at the Shrieking Shack, is attacked by the trio, and knocked unconscious. After explanations, Lupin, Sirius, Snape (unconscious), Harry, Hermione and Ron travel back to the castle with Peter Pettigrew tied between them.
The group arrives on the lawn, but Lupin transforms into a werewolf and in an effort to keep him at bay, Sirius transforms into Snuffles allowing Pettigrew to escape.
Harry and Hermione arrive in a clearing to find Sirius surrounded by hundreds of dementors. Harry attempts a feeble Patronus, but is saved by a mystery Patronus originating from someone across the lake--whom Harry presumes is his father.
Harry chooses to go outside now that it's getting dark to see if he can view his father from this side of the lake. After some time at waiting and seeing the attack, he realizes that he saw himself and performs the Patronus Charm, saving the past Harry, Hermione and Sirius from the dementor attack.
Snape gets all but Lupin and Pettigrew back to the castle. Black is detained upstairs and Harry, Hermione and Ron are put in the hospital wing.
Harry and Hermione ride Buckbeak to the correct window and give him over the Sirius, who rides the hippogriff to safety. They then run back to the hospital wing unseen.
Harry and Hermione awaken while Cornelius Fudge and Severus Snape discuss the capture of Sirius Black outside the hospital wing door.
Dumbledore enters the hospital wing and gives Harry and Hermione cryptic advice that "three hours should do." Harry and Hermione put the Time Turner around their neck and Hermione turns it three times, going back in time three hours. (The Harry and Hermione visiting the past will be indicated in purple.)
Harry and Hermione arrive outside the hospital wing and are let in by Dumbledore just as their past selves vanish into the past.