Hagrid probably brings him food.
Hagrid is most likely, as Fluffy's caretaker and the one who knows best how to get past him, the one to bring Fluffy his food. He often feeds the other dangerous creatures in his care himself, even the legal ones that aren't a secret, so it's logical he'd be in charge of feeding Fluffy as well.
“Well, I don’ s’pose it could hurt ter tell yeh that … let’s see … he borrowed Fluffy from me … then some o’ the teachers did enchantments … Professor Sprout – Professor Flitwick – Professor McGonagall –’ he ticked them off on his fingers, ‘Professor Quirrell – an’ Dumbledore himself did somethin’, o’ course. Hang on, I’ve forgotten someone. Oh yeah, Professor Snape.”
- Harry Potter and the Philosopher's Stone, Chapter 14 (Norbert the Norwegian Ridgeback)
However, it is possible that the house-elves could prepare food for Fluffy and have it sent up to his room using the same food-teleportation magic they use to fill the tables at the Great Hall.
However it's done, getting Fluffy food wouldn't be that hard.
If Hagrid's the one bringing him food, it'd be easy for him - he knows how to lull Fluffy with music, so if he needs to, he can just play him some music or sing him a song to get him calm while Hagrid brings in his food. Even if he tries to put the food in at first without playing music for Fluffy, he knows what to do if Fluffy gets too hard for him to handle.
“You’re the only one who knows how to get past Fluffy, aren’t you, Hagrid?’ said Harry anxiously. ‘And you wouldn’t tell anyone, would you? Not even one of the teachers?’
‘Not a soul knows except me an’ Dumbledore,’ said Hagrid proudly.”
- Harry Potter and the Philosopher's Stone, Chapter 14 (Norbert the Norwegian Ridgeback)
If, however, the house-elves are the ones preparing food for him, they wouldn't know that, but it wouldn't matter. They could send him his food exactly the same way that they send the food to the Hogwarts tables - by magic, without their physical presence upstairs. Hermione doesn't even know about them until her fourth year, so they don't necessarily need to go set anything up so they can send up food.