As soon as Harry sets off for Hogwarts, he meets Ron, as they board the train from Platform 9 3/4 at King's Cross ... and they meet Hermione shortly thereafter, when she barges into their train car looking for a lost toad. After an incident with an escaped troll in a girl's bathroom, the three become inseparable, which is when readers really learn about the personalities of Harry's two best friends.
Ron is often unserious, but very quick-witted, and even though he sometimes lets his jealousy or temper get the better of him, he's an incredibly good friend to Harry. Hermione is, on the other hand, extraordinarily serious, especially when it comes to school — she might not be the funniest girl in any given room, but she is the cleverest, and she keeps the two boys in line (and usually saves them with some powerful magic to boot).
Ron and Hermione, despite what Rowling says after the fact, complement each other wonderfully. Ron is able to lighten Hermione up a little bit, and she's always most drawn to him when he has moments of true thoughtfulness. The two kiss in the books for the first time after Ron says he wants to make sure Hogwarts' house elves are safe during the battle against Voldemort. Hermione, on the other hand, keeps Ron's more ridiculous impulses in check and grounds him. Her brilliance helps Ron become a better wizard, in that he learns powerful spellcasting right alongside her and Harry.
