To find out what version your system has, or if it has Java at all, open a Command Line Interface, and enter the command shown below. (In Windows, the CLI is called 'Command Prompt' and is located in the Start menu under Accessories. In Linux/Gnome, it's called 'Terminal' and located under 'System Tools'.)
If you get a 'command not found' message, or your version is less than 1.6, you will need to install the latest JRE. For Windows users, it's quite easy. Go to http://java.com/ and click on 'Free Java Download'.