At the risk of appearing really dumb, I must ask this question - as Americans we will fly into London, we will go through customs then, correct?, but then in several days time we will fly from London into Amsterdam, will it be necessary to go through customs again? And then when we fly out of Milan returning to London for our flight home, again, will we go through customs again at Milan and London, or no? Please advise, thanks so much.
Leslie

You go through customs only when you arrive in a country not when you leave. (Leaving Ireland for the US is different - since you're allowed to go through US customs in Shannon and Dublin airports.)

When traveling between Schengen countries you do not go through customs - since they are legally considered one "area" for immigration/custom purposes. The UK is NOT part of Schengen (although Italy and the Netherlands are) so yes, you will have to go through immigration customs when flying through.

I'm assuming you mean "go through immigration" rather than customs. When you arrive in London you will indeed need to go through a line of passport control -- called immigration. After that and after you collect your luggage you walk past a sign which says "nothing to declare" -- that's customs, which is "nothing".
You'll go past a similar "nothing to declare" station in Amsterdam -- again no big thing.
I believe you'll go through a passport control line at Amsterdam, anymore I'm sometimes surprised on inter European flights when you do or do not go through an immigration line.

In general, when you enter a country, you go through immigration (aka passport control) and customs.

When you exit a country, you go through immigration (with the noticeable exception of US, Canada and UK/Ireland).

UK and Ireland belong to a common travel area. So, going between the two is like going between two states in the US, no passport control.

15 other countries in Europe are part of the Schengen common travel area. So, no passport control among them usually, though sometimes individual countries can still set up checkpoints at entry. You can find the country list and more info at www.eurovisa.info.

When flying to/in Europe, bags are checked through to final destinations, and you only have to declare customs there, regardless of where you come from. This is unlike the US, where you have to claim bags at point of entry.

So, using the above info, we can answer the OP's question.

Flying US-London, immigration and customs at London.

Flying London-Amsterdam, immigration and customs at Amsterdam.

Flying Milan-London-US, if just transiting UK, then immigration at Milan, nothing in London, and then immigration and customs back in the US.

Security basically before every flight.

Thanks for taking the time to clarify this for me, it is as I suspected, just hope the lines are not too long and we don't have to waste a lot of time with all this business - we have sightseeing to do - again, thanks to all
Leslie

It's not the immigration and customs which will eat into your time, it is the security checks when you are leaving a country! allow plenty of time for those.