If you live in privately rented accommodation, either alone or with other full-time students only, you are exempt from Council Tax. You will need to apply for Council Tax Exemption Certificate every year and prove that you are a full-time student.
If you live with other full-time students, each one of you will need to apply for your own Exemption Certificate.
If you live with someone who isn't a full-time student, your accommodation will attract Council Tax, although the bill will be theirs to pay.