Hi,
I want to build a small system that is able to be controlled via the web,
for example, I want to be able to log on to any computer and check the
status of the system, be able to shut down the system and so on.
Does this work if I use the Arduino Nano 3.0 and the Arduino Ethernet Shield
rev3 or do I need additional hardware?
It depends on what this system is you want to shut down.
You will need a router with dynamic DNS(most do) and a DNS account(you should be able to find something free if you look hard enough, dyndns.org doesn't offer free accounts anymore). You will use a static IP for your ethernet shield, forward the necessary port in your router settings, and put your DNS info in the router. At this point you should have access to your arduino from any internet connection. Making a simple page with links that make the arduino do stuff should just be a matter of playing with it until you get something that works for you.
If you use the arduino nano you will need to interface with the ethernet shield with a breadboard.
So obviously there's more detail to it. But those are the things you need.
Thanks for your reply,
The idea is to be able to manage and control the boiler in my house when I'm not at home,
with 14 digital and 6 analog ports it enables to build in every possible unnecessary features
but like I said, I am a newbie and have many questions 
It might be better to use the Arduino Uno rev3 with the ethernet shield for not having to use the breadboard?
sorry for any spelling mistakes, I'm not so good at English so I write via google tanslate