If everybody in the house you're renting is a student then you don't have to pay anything.
If you're sharing with anybody that is not a student then there will be council tax due on the property (reduced from what it would be if everyone in the house was a student), but you personally don't have to pay it.
Don't forget to submit your council tax exemption forms (which usually have to be signed/stamped by your university) after you move in.