The EtherTen is just a tarted-up Uno and uses the standard Arduino IDE in exactly the same way - including all the libraries.. It requires its own driver for initial installation, as it is a unique third-party device.
You use the desktop to programme it via USB cable. The devices you are polling are usually connected separately by various means to the sockets provided.
The data is sent from the Ethernet and that is sent direct to the world. I use the cosm feed service for this, i.e. people go to cosm, not to me, and I guess it is the obvious approach for your project.