The article on Plugging In and Testing the Arduino Ethernet Shield shows how to connect and test an Arduino Ethernet shield.
In the article, an Arduino Ethernet shield is connected to an Arduino Uno board. The Arduino board is then powered up and connected to the network using an Ethernet cable. A sketch is loaded to the Arduino that configures it as a tiny web server.
A web browser can be used to connect to the Arduino web server. The web page that the server displays contains the values of the analog inputs of the Arduino. These values are updated every five seconds.