The HelloWorld example demonstrates how to get an Installation node, and call public methods within this class.
In the HelloWorldProgramNodeContribution check out this part:
private HelloWorldInstallationNodeContribution getInstallation() {
	return api.getInstallationNode(HelloWorldInstallationNodeContribution.class);
}
This is put into action in this case in the isDefined() method of the program node, in this way:
getInstallation().isDefined()
But in short, you could just do this:
api.getInstallationNode(YourInstallationNodeContribution.class).theMethodYouWantToCall()