Whenever I tell someone I am in a PhD Mechanical Engineering Program in USA, the next thing they ask is "When did you do your MSc?"... Good News: Almost all US Universities accept B.Sc Graduates into their MSc/PhD program with a fully funded offer+stipends
A CGPA greater than 3.5/5.0, Willingness to write Standardized Exams such as GRE, IELTS/TOEFL and tenacity to contact potential advisors.
My first advise would be to write the Graduate Record Examination (GRE). A lot of people dread this Exam, but I can tell you, it is very simple, provided you have the RIGHT resources and can put in the required time.
I prepared for this within a month while working and was able to do fairly well (Q:163,V:153, AWA:3.5) Trust me, when I say you can do way better than this, if you have the right resources and can give it enough time.
Having a First Class do not guarantee a Great GRE score, as a matter of fact, I have seen a lot of First Class Graduates fail this Exam due to the factors stated above. Its about tactics and strategy, I tell people when solving a GRE question becomes complex, You are WRONG.
Let us skip GRE for now (I can provide info on this on How to Ace the GRE quantitative). After passing the GRE Exam, proceed to write either TOEFL/IELTS. If you can pass GRE, TOEFL or IELTS becomes a walk in the park.
Once you have these Exams. Proceed to find Universities that offer your desired program. I have a reason for making this the second step.. Your results in those standardized exams, will enable you to make realistic University choices.
Some folks get a GRE score of 315 and they start applying to MIT, lol.. Be realistic if you don't want to waste your application fee and lower your admission chances. Do the Exams first and Select Universities (Another thread on this hopefully).
This is very important, even when your university graduate coordinator says you should not, please still go ahead. Reach out to Professors and let them know you like their research and would like to join their Lab. Their Research info. is on the University Website
Reach out to Current Students in that School, especially fellow Nigerians in that School. LinkedIn is an Excellent platform for this. Just type "Research/Teaching Assistant, University of Kentucky" and you get a list of students in that University, Nigerians First
They will better advice you on the admission process for that University and they can also share their experience with you.
Contact your graduate coordinator
Inform for your University Graduate Coordinator can be found on the School Website and they are always very helpful. They will also be able to tell you if there is funding for your program.
None of this was Planned. I did not wake up with the intent to do this. This is just reflex, So I can tell you that a lot of information may be missing in this thread article.