How do I obtain dual citizenship in the US and UK?

Either you are British or your not. Was your father born in the UK? What year were you born? Were your parents married? If your father is British not by decent, then all you need to do is apply for your British passport. Just as a side not. If you are wanting to go to Uni in the UK, please be aware that until you have been resident in the UK for at least 3 yrs, you will still pay international student fee's. (that is 3 times the home fee)

Uncle seems to have provided a good answer, and even provided a link that I was going to use. I just want to highlight that you seem to qualify for U.K. citizenship by descent http://en.wikipedia.org/wiki/British_nationality_law#British_Citizenship_by_descent. However, you may not want to qualify (or apply). You may be subject to a great deal more taxation. http://en.wikipedia.org/wiki/Multiple_citizenship#Taxation. Of course, if you are a student, then you may not be liable to or subject to the tax laws. Of course, if you are a student, then you may want to simply apply for a Student Visa.

you dont really obtain it ..., you become it http://britishexpats.com/wiki/British_Citizenship_by_Descent http://en.wikipedia.org/wiki/British_nationality_law http://www.ukba.homeoffice.gov.uk/britishcitizenship/eligibility/registration/noothernationality/