While a detailed description of every aspect of the size of Hogwarts is probably out of the scope of SFF, (See Richard's comment for one such theory, if you're interested.) I could try to list a few pointers.
Height (eight storeys plus the towers)
The highest floor ever mentioned is the seventh. (Although I can't find any clear quote that this is the highest.) Note that the ground floor isn't included, making there eight floors total. Extending past that is the towers with three highest being Ravenclaw, Astronomy, and Gryffindor.
Professors Flitwick, Sprout, and McGonagall are going to take groups of fighters up to the three highest towers—Ravenclaw, Astronomy, and Gryffindor—where they’ll have a good overview, excellent positions from which to work spells.
(Harry Potter and the Deathly Hallows - Chapter 31 - text available on Pottermore)
The highest tower is the Astronomy tower
The Dark Mark was glittering directly above the Astronomy Tower, the highest of the castle.
(Harry Potter and the Half-Blood Prince - Chapter 27)
There were a hundred and forty-two staircases at Hogwarts: wide, sweeping ones; narrow, rickety ones; some that led somewhere different on a Friday; some with a vanishing step halfway up that you had to remember to jump.
(Harry Potter and the Philosopher's Stone - Chapter 8)
Rooms (A lot?)
I don't know of any source for the the number of rooms in Hogwarts. As ThruGrog points out, Hogwarts really doesn't need more than fifteen classrooms, and there seems to be little need for an eight storey castle, but that is how it is.
HP-Lexicon has the following list of rooms in Hogwart mentioned in canon:
antechamber of the Great Hall, Armour Gallery, Astronomy Tower, Boys’ bathroom, Broom cupboard, Chamber of Secrets, Chambers of the Philosopher’s Stone, Charms classroom, Charms corridor, Classroom Eleven, Courtyard, Defence Against the Dark Arts classroom, Defence Against the Dark Arts teacher’s office, Disused classroom on the third floor, Dungeons, Entrance Hall, fifth floor corridor of the east wing, Filch’s office, Flitwick’s office, Girls’ bathroom, Great Hall, Gryffindor Tower, Head’s office, History of Magic classroom, Hogwarts corridors, Hogwarts grounds, Hogwarts kitchens, Hospital Wing, Hufflepuff common room, Library, Lockhart’s Office, Madam Hooch’s office, McGonagall’s office, McGonagall’s study, Moaning Myrtle’s bathroom, North Tower, Prefect’s bathroom, Quidditch locker room, Ravenclaw Tower, Room of Requirement, Seventh floor corridor, Slughorn’s office, Staff room, Third floor corridor, Transfiguration classroom, Trophy room, Unused 4th floor classroom storage for the Mirror of Erised, West Tower
JK Rowling drew a sketch of Hogwarts and grounds for the movie production which was shown in an extra for The Prisoner of Azkaban DVD (and later included in two behind-the-scenes film books).
More recently, a sketch that Rowling made for Bloomsbury has come to light which offers a different view. (Exhibited in Harry Potter: A History of Magic and tie-in books.)
Note that some recent editions of the Harry Potter books include a map based off of Rowling's sketches.