The well-known Erasmus-program that was introduced to increase mobility of students throughout Europe is also valid for Master degree studies. Students are financially supported for a 3- to 12-months period spent abroad.
The amount of financial support varies from country to country. But all Erasmus-students are exempted from paying any tuition fees, registration fees etc. As the grant mostly covers some of the living expenses, national grants or loans should be maintained during the stay abroad.
For those who are interested in doing their whole studies abroad, there is another program called Erasmus+ Master degree loans. Here students get a loan better than market interest rates that allows students two years of time to find a job before having to repay. The amount granted is up to 12.000 Euros for a one-year master program, or 18.000 Euros for a two-year master course.
For more information on the Erasmus programs visit the websites of the European Commission.