It probably depends entirely on the university that you apply to, and the country. Do your homework first and find out which are the best universities/departments for your subject. I'm doing Physics, so I'm not sure which are the top unis for Biology.

How do you feel about studying in a country where the language is not English? Having said that, in some countries such as Sweden, the Netherlands, and maybe some others the teaching at postgrad level is sometimes in English, due to the number of international students.

I think in the first instance you contact a potential supervisor in a department that interests you.