The serial number is the last six digits of the VIN (excluding any leading zero). For example, if your VIN were ZFFXR48B000123456 then your serial number would be 123456 (note that is not a real VIN and would, in any case, be for a Euro not a US car).
The VIN is on the steering column of a 355 and the door pillar - visible when the door is open.
The assembly number is on the lefthand side of the engine compartment (as you're facing the front of the car), about halfway down. It is a five-digit number on a small plaque.
The engine number is most easily found on the front page of the warranty card in the service book.