The Game of Thrones season 8 scripts have revealed how exactly Arya Stark managed to kill the Night King. In one of the biggest unpredictable twists in Game of Thrones season 8, the middle Stark daughter ended up being the one to defeat the White Walker leader at the climax of the dark and deadly "The Long Night."
The surprise was arguably paying off a lot of elements of Game of Thrones' story; prophetic lines like "what do we say to the God of Death" and killing "blue eyes" were retconned to refer to Arya's destiny, while her killing attack used light-footedness learned during her time with the Faceless Men, the catspaw dagger that had been repeatedly important, and a knife-drop trick last seen in her spar with Brienne in season 7 all came together in the attack. Of course, fans were still left with questions. How did this fit with the Azor Ahai prophecy (it doesn't really) and, perhaps more immediate, how exactly did Arya get a surprise jump on the towering Night King?
Game of Thrones season 8's making-of documentary, "The Last Watch", has provided an answer to the latter (the nature of prophecies will be debated for much longer). In a segment showing the cast script read, the directions for Arya killing the Night King - something that gets a big round of applause - is revealed, stating that Arya reached the iceman by jumping off a pile of dead wights:
"The Night King walks with methodical, terrifying calm. He stops before Bran and raises his sword to strike, but something is hurtling towards him out of the darkness. Arya. She vaults off a pile of dead wights, leaps at the Night King and she plunges the dagger through the Night King’s armor. The Night King shatters."
In the episode, Arya appears out of the mist to attack the Night King, with only a flutter of a White Walker's hair to hint at her presence. The script makes the appearance a lot more spacially logical. While there's not a lot of wight bodies shown on the ground (although it's hard to tell due to the episode's lighting), she clearly used them to gain a height advantage. It's a minor detail by itself but provides a bit more logic to the controversial Game of Thrones moment.
It's worth noting that this stage direction isn't totally accurate to the Battle of Winterfell episode; it doesn't include the Night King grabbing Arya or her knife-hand switch, suggesting that some aspects were altered by director Miguel Sapochnik during production. However, the corpse jump can still be assumed to be accurate to the intent.
The fact these questions are answered by the script says a lot about how the Arya twist was presented in Game of Thrones season 8, with writers David Benioff and D.B Weiss wanting her attack on the Night King to be as big a surprise as possible. They had her disappear for much of the episode's latter half in the hope audiences would forget about her, and presumably the jump wasn't shown to similarly play into the immediate shock. This has been a persistent criticism of season 8, but at least this answer shows smaller details were considered.
There's still a lot of unanswered questions about Game of Thrones' ending, including where Arya is heading when she travels "west of Westeros." And, while the cast and crew are talking opening about how the final season came together, we probably can't expect to get resolution to those big dangling threads until George R.R. Martin finishes the A Song of Ice & Fire books.