How do you become a US citizen through marriage if you live in the UK?

In order to obtain US citizenship, you must marry a US citizen in the first place. Your fiance must file a "fiance visa" which will award you temporary status in the US. You must then apply for permanent residency via the I-485 application (greencard.) Then, you must wait an indefinite number of years until you are eligible by law to become a naturalized US citizen.