If you don't see "Example Applet" in a yellow box, check that you have Java enabled in your browser. If Java is enabled, check that you have the Java runtime installed. If you don't have it, you can install the runtime from http://www.oracle.com/technetwork/java/javase/downloads/index.html.
If you can't see a red ball in a black square, you need to install Java 3D which you can get from http://java3d.java.net/binary-builds.html. This contains three jar files: j3dcore.jar, j3dutils.jar and vecmath.jar. Add these to your classpath. It also contains dynamic libraries for OpenGL graphics. You should add the directory containing these to your LD_LIBRARY_PATH.
In Windows you set these with Start, Settings, Control Panel, System, Advanced, Environment Variables. Then create or edit your CLASSPATH and LD_LIBRARY_PATH so that they include the locations of the Java 3D files you downloaded. For example, if you saved the files to C:\java3d then you would add C:\java3d\lib\ext\j3dcore.jar;C:\java3d\lib\ext\j3dutils.jar;C:java3d\lib\ext\vecmath.jar to your CLASSPATH and C:\java3d\j3d\bin to your LD_LIBRARY_PATH. Restart your browser and you should be able to see the Java 3D applet.
There are also extensive instructions from Sun.