Whether you need a special visa or residence permit to study abroad depends on your own citizenship as well as your destination. Different rules may apply to Danish and international students at SDU. It is important that you check the visa requirements by contacting the host university or the embassy of the country in question. Normally it is a mere formality to get a visa once you can document that you have been enrolled at a university within the country.
If you are an EU citizen and travel within the EU, you will normally only have to get a residence permit after arrival in the host country.
Outside the EU you will most likely have to apply for a visa, and normally you will be informed by the host university.
If you are a non-EU citizen you and you have a residence permit in Denmark, you need to check with the Danish immigration authorities whether you might lose your permit in Denmark by applying for a permit in another country.