I'm not familiar with Code Warrior. Java comes with a compiler called "javac". The simple way to do things is "javac MyProject.java", and it will create the .class file. You then say "java MyProject", and it will run the .class file.
I'm not sure that will work with whatever Code Warrior generates, which might be an elaborate package.
Honestly, unless you need this done yesterday, I'd ditch Code Warrior as it'll only serve as a crutch until you understand how the basics of Java work.
Sun (the maintainers of Java) have really good documentation on the language. They have a introductory tutorial online. I'd check that out. Here's the url:
http://java.sun.com/learning/new2java/index.html
Stick away from examples with Applets/Servlets. They'll just confuse you for now. Stick to Applications.