Whilst council tax tends to be not a problem with students in university accommodation, once you are out in private accommodation, you lose the protection of not being charged council tax. To not be charged council tax, you need to get an exemption form from your university. You usually get it from your general university reception, student advice centre, school/department office or your local council benefits and revenues office (addresses found on your local council webpage).
In order to not get a council tax bill, everyone in the house needs to get a council tax exemption form, and fill it in fully. There's a section which your university has to sign and stamp. Once this is complete, the forms need returning to the council offices as soon as possible.
If only one person in the house is liable for council tax, then everyone else should apply for council tax exemption and then the council tax gets discounted by 25%.
In Scotland, applying and receiving a council tax exemption due to your student status also makes you exempt from water charges, so it is vital you apply for this.