Visas and residence permits
If you have European citizenship and will study abroad within the EU you won’t need a visa. If you’re going outside Europe, or have non-European nationality, you generally will.
In most cases you will have to request a visa at your destination country's consulate in the Netherlands. You can only request your visa once you have been admitted to the university abroad. You will usually have to show your proof of admission as well as several other documents to consular staff. If you are unsure which documents to bring along with you always call the consulate in advance to check.
Work permits for internships
Within the European Union there is free movement of money, goods and people. Therefore if you are an EU national undertaking an internship within the EU you will generally not need a work permit. However countries can have additional requirements so always check carefully in advance. You can contact the EURES adviser (European Job Mobility Portal) of your destination country to request information on the rules that would apply to you.
If you will do an internship outside the EU, or have non-EU nationality, you will need to thoroughly research work permit requirements in advance to avoid unnecessary problems. In most cases you will need a work permit.
Both EU and non-EU students are advised to check the regulations that would apply to them in advance with their destination country's embassy in the Netherlands. The WilWeg.nl website also has handy Study Abroad - Information by country that can be very useful.