The answer to those Qs is different for every region. The meaning of AMP differs slightly from region to region. The SOP at the AMPs differs from region to region. As Sartre might put it, because location is such a fundamental determinant, "It truly is the Ace of Region."
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In NYC, where there just happens to be a place with the name you mentioned, first contact can be difficult, but I don't think it is as difficult as in LA or SF. Do not argue, bicker, or waste the time of the phone girls. If shot down, just try again another day. I was never asked for TER or P411 info (but I started years ago) but they might ask for other ID info. Once you are known and proven reliable, additional appointments will be much easier to schedule.
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You should be prepared to pay up front as part of the SOP. You will likely be taken to the massage room by mamasan or your hostess. She might leave briefly and come back with some towels or what not. If you are new, you will likely be asked for the (entire) fee that you give to your hostess. Now she will disappear for a few minutes: the mysterious waiting period. After she returns, she will help you prep for the table shower.  
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As the end of your visit approaches, you might hear a knock or a shout from mamasan as a reminder of the time. If time permits, you can shower again and your hostess will often help you get dressed. As you and she are ready to exit the room, that is a good time to slip her a tip for which she will thank you. She will escort you to the exit and out you go.  
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Ooops! I misquoted Sarte!