In Game of Thrones S08E03, we see Arya killing

the Night King.

How does she manage to sneak up on him given that he's surrounded by an army? Did she use the face of someone from the army?

Contrary to KharoBangdo's reasoning, I would theorize that Arya snuck up on the Night King in one of two different ways.

To get some other details out of the way, looking at the scene, I do not believe her flight angle is correct to imagine that she has been hiding in a tree this whole time, waiting for the Night King to approach. Yes, the screen is slightly tilted up from Bran's perspective, but as Arya is in flight, she seems to be flying straight for the Night King - and the momentum shift slightly before they make contact (and when the Night King catches her) makes it seem much more like horizontal momentum.

Anyway, here's really the detail that I think blows the whole 'waiting in a tree thing out of the water' -

You'll notice in the scene just prior to Arya revealing herself, one of the White Walkers notices something. The Walker feels a breeze, and you can see the Walker's hair get blown slightly (either by the wind or someone moving swiftly by). The Walker then looks to the right, as if the breeze came from there (or something / someone passed there).

This detail leads me to two theories:

1. That breeze was produced by Arya sneaking by. It's unclear whether or not she was making her dash straight to the Night King then or if she was making a dash through the tree line to remain relatively unseen while she approached (before making her big run up through the open ground). Perhaps some of her training from Jaqen was used here to be 'invisible' on her approach.




2. A little more far fetched, but not out of the question. The Walker is Arya, who simply feels a breeze and looks to the right. Arya is borrowing the Walker's face to blend in and get close to the Night King. The breeze (and the subsequent look) are an indication that something is about to happen - or perhaps that the time is right.

I think #1 is more likely, though I do hope they reveal a bit more about how this scene unfolded. Would be interesting to hear (or see) the scene from Arya's perspective.

At the very least, I do feel like there is some level of significance from that subtle breeze and motion the Walker makes just prior to the Night King dying. The sound of wind blowing rises up slightly over the dramatic music, and I'd like to think that was a purposeful touch.

There are a lot of trees in the Godswood. She was hiding on top of one of them. Hence, she could sneak up on Night King and jump from above.

The angle at which Arya jumps & the way Night King catches her, indicates that she can't do it from the ground. Also, the Night King was away from the castle walls. So, a tree is a logically correct deduction.

When Arya meets Melisandre inside the castle, she tells Arya that she will shut blue eyes. This is to prophesise the Night King's death.

Melisandre ask Arya: "what do we say to the God of Death?" She says "Not today" and walks off. Arya understands clearly what needs to be done and she goes away from the battle to hide in a tree as she knows that the Night King will come for Bran in the Godswood.

Unclear.

One of the most popular theories going around right now is that she disguised herself as a walker to get close.

This does seem like a plausible explanation.

We know that Arya's training under the guidance of her former mentor, assassin Jaqen H'ghar, taught her how to successfully wear the faces
of others, enabling her to get into places that she couldn't if she
looked like herself.

So, is that what happened there? Did Arya disguise herself as a White
Walker so that she could sneak into the Godswood entirely undetected
and then, when the time was right, slay the head zombie?

A lot of people are convinced that that was how she slipped in undetected and did her very worst.

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_{Is this how that dramatic Game of Thrones moment really happened? - DigitalSpy}

Among other explanations, it's believed that she was noticed.

There is a moment, right before the Night King is about to kill Bran, when the camera pans to one of the White Walkers stood behind him, who then turns their head to the side.

It's a minuscule detail – if you weren't paying attention you could very easily have missed it – and some might argue that it was entirely insignificant. But then again, is anything on GoT done without significant reason? [...]

There's every chance that the other White Walker, by moving his head, had picked up on Arya's presence. But by then it was too late. She was already mid-air and the Night King had turned around to face her and finally meet his maker.

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_{Is this how that dramatic Game of Thrones moment really happened? - DigitalSpy}

So, in conclusion there are various different possible explanations.

The sneak attack was merely a diversion--presumably Arya and Melisandre know one can't sneak up on the Night King.

Strategically, it was a feint, allowing her to get close enough to the Night Kind to kill him. The way the shot the knife dropping from her hand while she is being choked strongly implied she was losing consciousness or dying, only to have it revealed as a stratagem.

This was foreshadowed by Lyanna Mormont's killing of the undead giant earlier in the episode.

The producers may not have considered it strictly necessary to show how Arya got positioned for the sneak attack since it was merely a narrative device. The more meaningful aspect is that Theon's self-sacrifice bought her them all time.