The chessweb server runs in any J2EE application server supporting the servlet 2.4 specification. At the time of writing, the chessweb server has only be tested on Tomcat v5.5.
Download the latest distribution from here. Next copy the chessweb.war file into Tomcat's webapps directory. Make sure Tomcat is running and that should be it.
For details of installing Tomcat, please refer to the Tomcat documentation.