Next step - find the Admission Office - they'll give u contact information of an Adviser, who will know for sure what are the exact requirements for the application from ur country and they will go through everything with u step by step. Keep their phone # - it will save u hours of web search!
At North Park the Admission Officer was the same for residents and international students. At UTSA and U of M there is a specific department that deals with documents for international students (visas, DSs, I20s, etc).
The deadline for application is mostly different for every university - make sure u know them all. Sometimes it is even different for every single college inside the university - once again, make sure u know ur specific dealines!
Unlike ukrainian universities here u can start at both spring, fall and in some cases summer semester. One thing to start with way beforehand is TOEFL. It's valid for two years but in case u mess up on one of four sections of the test u can retake them individually without taking the whole test again. U are required to register at least 3 weeks before the test. Give it another two weeks to get the results.