OK - there are two extra controls on an international arrival ...
a) Immigration, where you need to be able to show that you're there for the reason on your visa (or for a reason that doesn't need a visa)
b) Customs, where you need to be able to show that you're not trying to bring anything illegal in or make an import - particularly commercially - and avoid local tax.
Check in is just the same, hand baggage just the same, as a USA internal flight except that the airline will want to see your passport just to make sure that you won't be turned back at their expense at London
You're visiting for a short while. You're a Bona Fide visitor. The UK welcomes American tourists. You'll naturally have proof of where you're going, excitement, plans, papers, a return ticket. I don't think you'll have any problems at immigration; problems typically come if something you say or something in you manner gives rise to suspision .... and the immigration folks are trained to tell the folks trying to avoid or stretch the system from those merely scared at thier first short visit.
Customs, you can usually just walk straight through. A customs officer may stop you and have a quick chat (I've never had more that "where are you coming from" or "how long have you been away") but not usually anything more. You can bring in whatever personal effects you need for your trip, I think it's $100 or $200 of gifts (someone else, please remind me), a litre of spirits, 200 smokes, a certain amount of perfume. 200 cigarretes + 10 in a half smoked packet would NOT be a problem, but 2000 (note the extra 0) would be. And - no banned substances, and these days they're pretty hard on meat, fruit, veg according to the signs but nothing like as bad as when you go back into the states.
Summary - I would be very suprised if you had more that a minute's chat with the immigration officer, and I would be suprised if you got stopped at all at customs. And you're going to be so in the rules you'll sail straight through. Have a great flight and a great time,