If you're already married, the process would be:
-apply for a Spouse Visa (good for 2.5 years) from the US
-just before those 2.5 years are up, apply for further leave to remain (also valid for 2.5 years) from within the UK
-just before those 2.5 years are up, apply for indefinite leave to remain (valid indefinitely)
-once you have been living in the UK for three years (including the time since your Spouse Visa) and hold indefinite leave to remain, you can apply for UK citizenship and a passport
Of course it's not quite as simple as that (the Spouse Visa has strict financial requirements now), but that's the basic timeline. 5 years from Spouse Visa to Citizenship.
