First of all, you will need a white collared shirt, a neck-tie in your house colors, and a grey sweater vest. If you are male, you need a pair of black pants. Girls can either wear black pants or a black skirt and white knee socks. both genders need black dress shoes. If the girls are wearing skirts, they should wear mary janes. You will also need a long black cloak. An old graduation cloak works perfectly.
One problem we encounted while making this costume was the lack of ties in the proper house colors. This can be solved by buying a solid colored tie and painting the opposite colored stripes on it with fabric paint or a paint pen. My brother bought a silver tie at Goodwill and painted green stripes on it.
The next detail to cover are the character specifics. If you are Harry, you will definatly want to have glasses. You may even want to look at hair color. If you don't want to go so far as to permanently die your hair (which most people won't), Sally's Beauty Supplies sells none permanent spray on hair color in natural shades for about three dollars a can. This step is for the more noticable character colors, like the Weasleys. Also, you will want to consider wether or not your character is a Prefect. If he/she is, you will want to make a Prefect badge. Will made his using a bit of cardboard, which he hot glued a safety pin to the back of. before gluing the saftey pin on, he shaped the cardbard into the shape of shield and wrote "Hogwarts Prefect Tom Riddle" in green ink, then drew a snake. this badge is not completely accurate to the series. if you want a more accurate badge, check the chapter of Harry Potter and the Order of the Pheonix titled "Mrs. Weasly's Woes," and follow the pattern listed there.
Other ways to make your costume more character specific is to think about items your character might have on their person (things they carry around with them). Hermione, for instance, would carry around large books with titles like Hogwarts; A History. You can amke this by making a book jacket for another book. Will, as Tom Riddle, carried aroung a tattered book which he refered to as his journal. Also, every student needs a wand. Instead of buying a cheesy expensive electronic wand, get a decent sized stick from outside and whitle it into the proper shape, or you can leave it in it's natural form, like my brother did..
Ta-da! You're now ready for the Wizarding World!