The counter agent in Detroit should ask you if you want your luggage checked through to your final destination, Rome. If the agent doesn't ask, then you need to mention it to the agent. There's no need for you to pick up your luggage and recheck it in AMS. Since you are on NW and KLM, which code-share their flights, there will be no problem with this. The counter agent in Detroit will also give you boarding passes for the Amsterdam-to-Rome flight. Thus, at AMS, all you have to do is find the gate for your connecting flight. And check out the cool Lego version of Schipol airport, in AMS!
Once you get to Rome, claim your luggage and go through customs. Which means that, as long as you have nothing to declare, just walk through the green, "Nothing To Declare" lane.
In AMS, you may have to go through several security checkpoints, depending upon what gate you arrive at and what gate you depart from. You could very well have to go through immigration also, again, depending upon the gates. My experiences in AMS have been that everything is run efficiently, so 3 hours should be plenty of time.
