You can easily add Internet-based control for your Arduino if it is close enough to your server to be connected via USB. This tutorial will give the basics you need to get it working.
The gist of this method involves a webpage that includes PHP elements. When one of those elements is manipulated, a command is sent via serial connection to the Arduino which then reacts based on what it received. This example uses an Ubuntu box that is running an Apache server. The Arduino sketch sets up the serial connection and then listens for incoming traffic. Whenever it receives a non-zero character an LED will blink. On the server side of things you’ll need to make sure that the system user that runs Apache (www-data) has permission to write to a serial port.
This base example may seem extremely simple, but there’s no end to what you can build on top of it. Different PHP events can be added to push new commands over the serial connection with matching test conditions added to the sketch.