Non-EU citizens will need a valid passport when visiting Sweden. Citizens of the EU/EEA states need a valid passport or a National ID card. Make sure that your passport is valid for the whole period you will be staying in Sweden.
For EU/EEA citizens:
If you work, study or have sufficient means to support yourself, you automatically have right of residence in Sweden and therefore need not register with or apply for a residence permit at the Swedish Migration Agency.
For non-EU/EEA citizens (incl. UK citizens):
You must have a visa before entering Sweden. You will have to apply two to three months before departure at the nearest Swedish embassy or consulate. Do not leave for Sweden without a student visa!
You should also make two copies each of your "Meddelande om beslut" from the Swedish Migration Board, and your Swedish visa. Leave one copy at your permanent address when you go abroad. Carry the other copy in a place other than where you usually carry your passport. Should your passport be lost or stolen, you will then be able to provide the authorities with the necessary information.
Nordic citizens do not require visa or residence permit.