Fulbright Program enables graduate International students, professionals and artists from outside USA to study in one of US universities / institutions for one year or more.
To apply to this Scholarship you should be a residence for one of the countries in the following link: http://foreign.fulbrightonline.org/applicants
Applications for 2016-2017 starts to open on 1st quarter of 2015, depending on your country, to check that you should try to contact US Embassy in your home country, usually before the end of October.
It is good to visit the county website for more information.
Here is the official Fulbright website: http://foreign.fulbrightonline.org/about/foreign-fulbright