Home automation with Arduino is surprisingly easy, and remote-control via the Internet is also possible. However doing so requires knowing what the public IP address of your home connection. In most cases this address is dynamic, that is it changes at the whim of your ISP - and thus you need to change it in your remote-control app (etc) as required.
This can be a pain, however one solution is the use of an Arduino and a small Android app by Instructables member xlisus. They've provided a small sketch to run on an Ethernet-enabled Arduino which is connected to your home router, which broadcasts the public IP back to the Android phone via WiFi and the router. This is then accessed via the Android app.
When putting together your next Internet-enabled Arduino or AVR project - save time, space and money with the Freetronics EtherTen . Apart from being fully Arduino Uno-compatible , it has onboard Ethernet, microSD socket, full USB interface (so you don't need a costly FTDI cable just to upload a sketch!) and supports optional Power-over-Ethernet.