Iridium is written against Java 8, which must be available on your PC before you can run the application.
You may have seen references to this chapter talking about trusting the location where the JAR file is downloaded from. This used to be necessary when the JAR file has a self signed certificate, but it now signed by a trusted certificate, so adding a trusted location in the Java Control Panel is no longer necessary.
You will want to enable the Web Start console. This gives you feedback on how the script is running.
Open the Java Control Panel, click the Advanced tab, and select the Show Console option.
The first time you run the application in Windows, you may be prompted to allow it to access the network. Click the Allow access button if you see this prompt.