Contact the British Consul in New York City for full details on what is required to establish British residence. Be advised that citizenship may only be applied for after five years continuous, legal residence in the UK. I might add that the cost of living is considerably higher in Europe (including the UK) than it is in the United States. You may also wish to take legal advise concerning the status of your US citizenship should you choose to take up foreign nationality. Finally, it has been my observation that there is a considerable cultural gap between individuals brought up in the USA and those native to the UK, and this often proves to be insurmountable. I will give you one example:

Suppose you are 25 years old and grew up in the United States. You will have missed out on 25 years of grass roots "pop" UK culture. You won't know any of the soap operas, what music was cool, or what teams did what, when. You won't have grown up with kids TV, Top of the Pops, the Beano, or Christmas Pantos. You won't know any of the TV presenters, you won't get most of the jokes. You will have very little in common with your peers. Ultimately you will be a stranger in a strange land. And by-and-large that is how you will be treated.