If you are just finishing NYSC and would love to travel abroad, this should be your to-do list:
1. Get the list of all available local and Int'l scholarships.
2. Look for all schools in the world that offer the course you like.
5. Get unofficial transcript or pdf of your undergraduate courses.
6. Apply for Int'l passport.
7. Get atleast 3 lecturers in your school who will write references for you. This is the most arduous task. One way to go around this is to find their contacts from your ex-class mates and establish relationship with them now before you request for their letters.
8. Fix a date for any of the exams. A fixed date will make you more serious. You need an average of 4 weeks for TOEFL and 4-6 months for GRE depending on your level. GRE will give you an edge if you specifically want USA. You can do free mock exams to first know your level.