JavaS3Backup is started using webstart. Simply click on this link to start it: http://js3backup.dgunia.de/webstart/javas3backup.php.
You need to have Java 1.5 installed. And to use better encryption, you should install the Java Cryptography Extension (JCE) Unlimited Strength Jurisdiction from http://java.sun.com/javase/downloads/index_jdk5.jsp at the bottom of the page. You can use this download for Java 5 and 6. Simply unpack the downloaded archive and put these replacement files into your jre/lib/security directory.