Visit To America.

You are eligble to apply fo a United States visa in the UK. However, the embassy requires to see STRONG TIES to return to the UK after your visit, as the immigration act states that all applicants for non immigrant visas are presumed to be intending immigrants to the US. This strong ties are social, economic and or family ties outside the US.

They look at things like:
How long have you been in the UK? (the longer the better!)
How long have you been at your current address?
How long have you been at your current job?
Are you, or are your children enrolled in school?
What ties do you have in the Uk?
What commitments do you have in the Uk that would compel you to return to the UK?

Now, since you are a student, your strongest tie will be your studies so you will need a comprehensive letter from your school detailing your course, length of study/proposed course completion date, degree that would be earned e.t.c. I would also suggest that you should have been resident in the UK for at least 6 months before applying to show that you are at least "settled" in the UK. You will also need a very good sponsor for your trip/show your funds or show that you will be staying with someone in the US. If you already have a job lined up for you on graduation, you can tender evidence of that also.

Overall, I would tell you that it could be as difficult in the UK as it is in Nigeria so you may think carefully about applying. It doesnt matter how full your passport is with visas or whether you have travelled to the US before. Once you do not meet their conditions as related to the requirements above, then you will not be given a visa.

If you do apply, you will need to call to book an appointment and they will tell you the next available date. You will also pay the visa fees via phone using a debit/credit card and then they will send you an e-mail PDF receipt/interview confirmation providing further instructions for the interview. On the appointment date, you will go along with the receipt/document sent to you, your passport, a photograph and your vital documents. See link for further details.

http://london.usembassy.gov/cons_new/visa/niv/index.html