Using Arduino Yún to send data through Ethernet
There are three bits of information you need to know:


The Ethernet port is connected to a tiny Linux computer
On Linux you can do HTTP POST and HTTP GET using a program called cURL
The AVR chip can tell the Linux computer what to do using the Process library.


Putting all those together: You need to use the Process library to tell Linux to run curl with the right parameters.

Just like the tutorials show you:


https://www.arduino.cc/en/Tutorial/Process