Applying to Swiss grad school from America: Advice?

I'm a math major in US and I'm interested in applying to EPFL in Switzerland for grad school in computational sciences and engineering. I have asked around my university for advice but nobody knows about applying to European institutions and what they look for in a student. While I have all the prerequisites mentioned on the program's website I don't know what I can do to further improve my application package.

So far I have a mid 3.6/3.7 GPA, I've done research at NASA for two summers, studied math abroad in Europe and am working on research in computational fluid dynamics.

Does anybody have any experience in applying to swiss schools for masters programs and would anyone care to share some advice?