Before you can run Zinc you must have installed a Java 2 Runtime Environment version 1.4 or greater. You can find out about the J2RE at the Java website. Be sure that you install version 1.4 rather than an earlier version.
You will also need a graphical environment in which to play Zinc. If you are using Windows then you will have this. If you are using UNIX then you will need to have X installed. Without a graphical environment you can only run a headless server.