There are many ways of getting information from an Arduino to the outside world, and a simple and easy to understand method is via local area networks or the Internet with an Ethernet shield or Ethernet-enabled Arduino board. To get up to speed on this method you can follow the Ethernet tutorial from the tronixstuff website. In their latest update the reader starts with testing Ethernet shields with Arduino, to creating a simple webpage in order to understand how to display data from a web page over a LAN.
Finally after some discussion about static IP addresses you can learn how to create websites that will display sensor data that can be viewed from any web-enabled device on the Internet, for example a mobile phone:
If you need an Ethernet-enabled Arduino, save time, space and money by using 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.