There is a programme called the Fulbright programme for postgraduate students. It is both for students from the US and students looking to study in the US.
The United States has many scholarships for International Students, you just have to find them. Write to some Universities in the US and ask for advice about funding. There are books and books of scholarships at the library... There is a scholarship for just about everything you can think of.
If you play sports, then you do not necessarily have to be the best to get a sports scholarship... Some of the top schools in the US in terms of academics do not have top sports teams, and so they will often give scholarships to students who might just be dedicated and pretty talented players.
In my state, Florida, if you have been a resident (note: not necessarily a citizen) for at least a year (I believe) then you can get the state rate, which is about 1/5 the cost of what out-of-state students pay.
Good luck!