Siri is an app for Apple's iPhone 4S. It is best described as an intelligent virtual personal assistant and can also be called a knowledge navigator. It works as part of the phone, so you don't really need to know much to use it.
When you turn on your new iPhone, you will be prompted to use Siri automatically, so all you have to do is select Yes. You will also be asked what language you want to use (this also includes different varieties of English eg US or UK.) You then select various other options such as whether you want to hear or read Siri's answers to your questions, or what information you want stored in the app.
The setting that controls Siri can be found under the general Settings tab.
If you click here you will find an overview of how to start using Siri, and below the main article - in the 'Dummies Recommends' section, bottom left - are links to more specific information on exactly how to use it.