Sarah smiles. "Thank you."

"Move along now," says a sharp voice coming from the door—McGonagall, returned. "The Sorting Ceremony's about to start." One by one, the ghosts float away through the opposite wall. "Now, form a line," she tells the first years, "and follow me."

She gets in line.

They walk out of the chamber, back across the hall, and through a pair of double doors into the Great Hall.

It's lit by thousands and thousands of candles that are floating in midair over four long tables, where the rest of the students are sitting. These tables are laid with glittering golden plates and goblets. At the top of the hall is another long table where the teachers are sitting. Professor McGonagall leads the first years up here, so that they come to a halt in a line facing the other students, with the teachers behind them. The hundreds of faces staring at them look like pale lanterns in the flickering candlelight. Dotted here and there among the students, the ghosts shine misty silver. Instead of a ceiling, there is a velvety black emptiness dotted with stars, the Great Hall looking like it simply opens on to the heavens.

Professor McGonagall silently places a four-legged stool in front of the first years. On top of the stool she puts a pointed wizard's hat. This hat is patched and frayed and extremely dirty. Aunt Petunia wouldn't have let it in the house. 

For a few seconds, there's complete silence. Then the hat twitches. A rip near the brim opens wide like a mouth—and the hat begins to sing:

Oh, you may not think I'm pretty,
But don't judge on what you see,
I'll eat myself if you can find
A smarter hat than me.

You can keep your bowlers black,
Your top hats sleek and tall,
For I'm the Hogwarts Sorting Hat
And I can cap them all.

There's nothing hidden in your head
The Sorting Hat can't see,
So try me on and I will tell you
Where you ought to be. 

You might belong in Gryffindor,
Where dwell the brave at heart,
Their daring, nerve, and chivalry
Set Gryffindors apart;

You might belong in Hufflepuff,
Where they are just and loyal,
Those patient Hufflepuffs are true
And unafraid of toil;

Or yet in wise old Ravenclaw,
If you've a ready mind,
Where those of wit and learning,
Will always find their kind;

Or perhaps in Slytherin
You'll make your real friends,
Those cunning folk use any means
To achieve their ends.

So put me on! Don't be afraid!
And don't get in a flap!
You're in safe hands (though I have none)
For I’m a Thinking Cap!

The whole hall bursts into applause as the hat finishes its song. It bows to each of the four tables and then becomes quite still again.

That was an interesting song. It seems to reinforce her thinking that Ravenclaw or Hufflepuff would fit her best.

She claps but she's kinda confused why the hat is dirty. Do magical objects resist cleaning?

Professor McGonagall now steps forward holding a long roll of parchment.

"When I call your name, you will put on the hat and sit on the stool to be sorted," she says. "Abbott, Hannah!"

A pink-faced girl with blonde pigtails stumbles out of line, puts on the hat, which falls right down over her eyes, and sits down. A moment's pause—

"HUFFLEPUFF!" shouts the hat.

The table on the right cheers and claps as Hannah goes to sit down at the Hufflepuff table. The ghost of the Fat Friar waves merrily at her.

Sarah smiles and claps enthusiastically. She'll clap for other students too, perhaps not quite as enthusiastically for Gryffindor and Slytherin.

The Deputy Headmistress continues down her list: Kellah Bimm, Gryffindor; Susan Bones, Hufflepuff; Terry Boots, Ravenclaw; Mandy Brocklehurst, Ravenclaw; Lavender Brown, Gryffindor; Millicent Bullstrode, Slytherin; Vincent Crabbe, Slytherin; Justin Finch-Fletchley, Hufflepuff; Seamus Finnigan, Gryffindor; Gregory Goyle, Slytherin. Some of them the Hat decides on immediately, while others take a bit longer.

After those: "Iroko, Adedayo!"

And Dayo confidently strides towards the hat and puts it on.

Sarah smiles widely.

The hat stays on Dayo's head for almost a minute, and then—

"SLYTHERIN!"

He beams, takes the Hat off, and walks towards the applauding table.

She claps loudly for him. Hopefully that will be the right decision for him.

Neville is, after some deliberation by the Hat, a Gryffindor, to his own surprise. He runs off still wearing the Hat and has to return amidst laughter to give it to 

"MacDougal, Morag!"

Who is a "SLYTHERIN!"

Malfoy goes next, and the Hat has barely touched his head when it cries—

"SLYTHERIN!"

—and he swaggers his way to Crabbe and Goyle, who are apparently friends of his.

She's glad Neville ended up where he wanted. She doesn't give much thought to Draco but claps politely.

Moon, Nott, Parkinson, Patil (Padma), Patil (Parvati), Perks—

—and then, "Potter, Sarah!"

And whispers suddenly break out like little hissing fires all over the hall.

"Potter, did she say?"

"The Sarah Potter?"

She smiles and does her best to look confident as she walks up to the front of the room and puts on the hat.