The installation of Firebird on Windows is easy as there is an installer for it which you can download at Firebird File Repositories.
On platforms that are service-capable (NT, XP and forward) Firebird will be installed by default as a service. That means Windows will start it automatically every time it boots, unless you configure it otherwise. In older platforms (Windows Me and prior) that do not support services Firebird runs as an application and the Firebird Guardian takes care of booting it.
The installation process of Firebird depends on whether you want to use Classic, Superserver or Embedded architecture. If you do not know yet which you prefer go for Superserver since it is the recommended one for Windows. As Andrei suggested, though, you should check which one fits your needs best.
To check that the Firebird Server is running in Windows just go to Services applet and check for Firebird Server and Firebird Guardian services. Alternatively, if you used the installer Firebird will have installed a Server Control Applet in the Control Panel.
You can find more information on this matter in Firebird Documentation Index.
Referring to the example database the answer is yes. Firebird comes with the employee.gdb database, which you should find in the Examples subdirectory of your Firebird installation. To connect to it follow the steps in Connecting to the sample database