How did Harry get his hair cut at Hogwarts?

In the first book, it's mentioned several times that Harry's hair grows quickly. I don't remember he exact quote, but I remember something like 'he must have gotten more haircuts than all the other boys in his class combined,' and Uncle Vernon mentioning that he needs a haircut every couple weeks.

Where does he get it cut at Hogwarts? For that matter, where do any of the student at Hogwarts get their haircuts?

Here's the quote from The Deathly Hallows that shows that Harry's hair grows long when it's not cut:

His face was huge, shiny, and pink, every feature distorted by Hermione's jinx. His black hair reached his shoulders and there was a dark shadow around his jaw.
_{-Harry Potter and The Deathly Hallows, chapter 23: Malfoy Manor}

Answer

TL;DR:

Harry's hair doesn't grow extraordinarily fast; it only regrows magically fast in response to the unwanted haircuts he receives. So there is no need for special barber arrangements at Hogwarts; Harry gets his hair cut the same way as the other students.

Uncle Vernon on Harry's hair

Uncle Vernon entered the kitchen as Harry was turning over the bacon.
"Comb your hair!" he barked, by way of a morning greeting.

About once a week, Uncle Vernon looked over the top of his newspaper and shouted that Harry needed a haircut. Harry must have had more haircuts than the rest of the boys in his class put together, but it made no difference, his hair simply grew that way — all over the place.

_{Harry Potter and the Philosopher's Stone, chapter 2, "The Vanishing Glass"}

While this could be interpreted to mean that Harry's hair grew exceptionally fast, necessitating a haircut every week, a far more likely interpretation — especially in light of the treatment Harry receives from the Dursleys — is that uncle Vernon simply takes every opportunity to be mean and abusive to Harry, who looks nothing like his beloved son, Dudley.

Harry vs Dudley

In the same chapter, we get descriptions of both Harry and Dudley.

(...) Harry had always been small and skinny for his age. He looked even smaller and skinnier than he really was because all he had to wear were old clothes of Dudley's, and Dudley was about four times bigger than he was. Harry had a thin face, knobbly knees, black hair, and bright green eyes.

_{Harry Potter and the Philosopher's Stone, chapter 2, "The Vanishing Glass"}

And, as quoted above, "his hair simply grew that way — all over the place."

Contrast this with Dudley, who as sleek and smooth blond hair:

Dudley looked a lot like Uncle Vernon. He had a large, pink face, not much neck, small, watery blue eyes and thick, blond hair that lay smoothly on his thick, fat head. Aunt Petunia often said that Dudley looked like a baby angel — Harry often said that Dudley looked like a pig in a wig.

_{Harry Potter and the Philosopher's Stone, chapter 2, "The Vanishing Glass"}

So Harry looks nothing like Dudley, and neither does his hair. Yet another reason for uncle Vernon to verbally abuse Harry.

The haircuts — and lack thereof

Once, Aunt Petunia, tired of Harry coming back from the barbers looking as though he hadn't been at all, had taken a pair of kitchen scissors and cut his hair so short he was almost bald except for his bangs, which she left "to hide that horrible scar."
(...)
Next morning, however, he had gotten up to find his hair exactly as it had been before Aunt Petunia had sheared it off.

_{Harry Potter and the Philosopher's Stone, chapter 2, "The Vanishing Glass"}

If Harry's hair grew this fast all the time, he'd need a haircut every day to not end up with hair down to his knees. But that doesn't happen. That is because Harry's hair doesn't grow extraordinarily fast; it regrows magically fast in response to the unwanted haircuts he receives, either from the barber or from his aunt Petunia.

Note that the book doesn't mention aunt Petunia having to cut his hair to keep it in check; she simply wants to cut it because she doesn't like it the way he wears it.

A couple of lines further on in the chapter we read how a sweater Harry doesn't want to wear magically shrinks. Yet his other clothes do not shrink all the time.

Conclusion

There is no need for special barber arrangements at Hogwarts. Harry can get his hair cut the same way as all students.

Magical haircuts

No mention is made how Hogwarts students — or indeed wizards in general — have their hair cut, but it can be done by magic, as the following quote shows, although it doesn't rule out that it is done mechanically as well.

It provided a distraction, watching Mrs. Weasley force Charlie into a chair, raise her wand threateningly, and announce that he was about to get a proper haircut.

(...)

Charlie approached, running his hand slightly ruefully over his new, brutally short haircut.

_{Harry Potter and the Deathly Hallows, chapter 7, "The Will of Albus Dumbledore"}

Shaving

Another quote from the same chapter shows that shaving may involve magic as well.

The other packages contained an enchanted razor from Bill and Fleur ("Ah yes, zis will give you ze smoothest shave you will ever 'ave," Monsieur Delacour assured him, "but you must tell it clearly what you want... ozzerwise you might find you 'ave a leetle less hair zan you would like...") (...)

_{Harry Potter and the Deathly Hallows, chapter 7, "The Will of Albus Dumbledore"}