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.
You can start by checking this:
4icu.org
3. Start preparing for TOEFL, GRE or IELTS, check ets.org for all the info you need.
4. Learn how to write good SOP/motivation statement.
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.