The format is:
International Access code/prefix; Destination country code; full number including std.
So, from the states it's 011, then country code, then 161xxxx or whatever.
You take off the leading zero of the std code because that's not part of the phone number. The leading zero is our 'long distance access code'/long-distance prefix or whatever they call it. It's to signal to BT that you're about to give an std/area code.
So in the UK we have the following codes:
International prefix: 00
Long distance prefix: 0
example area codes: 161, 207, 207, 113 etc.
That's why when your computer asks you what your area code is, you should never put in a zero. I am forever changing it from 0161 or 0113 to just 161 or 113 on peoples computers.