The servlet runs inside of Tomcat, so to run the servlet you need to install Tomcat. We would suggest getting the most recent version of Tomcat from here. Make sure it's 5.0.19 or greater as we've had problems with versions as recent as 5.0.9.
Once you have Tomcat installed, you'll also need to make Tomcat use JacOrb instead of its built-in orb. You can do this by copying the JacORB jars out of wily/repository/JacORB/jars into the common/endorsed directory in the base of your Tomcat install. The necessary JacOrb jars are antlr-2.7.2.jar, avalon-framework-4.1.5.jar, concurrent-1.3.2.jar, jacorb.jar, logkit-1.2.jar and wrapper-3.0.3.jar. By doing this, all other servlets in this instance of Tomcat will use JacORB instead of the built-in java orb. So, if you have other CORBA servlets that you don't want to use JacORB they'll need to be in a separate instance of Tomcat.
With Tomcat setup, now all you need to do is move the wily.war file included in the wily directory of wily-1.0.tar to the webapps directory of in the base of your Tomcat install. If Tomcat is running, once you drop it in there Tomcat will pick up wily.war, expand it and make Wily available at /wily/Check at the base url of your Tomcat install. If it isn't running, it'll find and expand wily.war the next time you start Tomcat.