The ethernet client just sends text to the port on the server that is listening for http requests.
when you see a line like:
client.println("GET /search?q=arduino HTTP/1.0");
Its sending GET /search?q=arduino HTTP/1.0 in clear text to that port.
It represent what you would normaly see in the address bar of your browser.www.google.com/search?q=arduino
The examples then send clear lines or carriage returns at set points to tell the listening web server that all of the request has been sent and you are ready to receive the results.
The results then come back in clear text with http headers followed by the html markup.
So the overall idea is to use the ethernet library to send and receive the clear text characters following the http protocols.
You then need to process the html returned to do what you want with the information.