From one applet, how do I communicate with another applet loaded from the same server?

It really doesn't matter that they are loaded from the same server, as long as they are running in the same JVM in the browser, you can call methods between them.

If you include a name="appletA" value in the applet tag of the applet you want to call methods on, you get a reference to it by using the AppletContext:

MyApplet appl = (MyApplet) getAppletContext().getApplet("appletA");
if (null != appl) {
    appl.register("Hello there!", this);
}