The gist really comes down to this:
1. install tomcat (e.g. with your distributions package manager)
2. uncomment the respective block, and set the admin account roles and password in server.xml
3. go to the admin interface (usually /manager)
4. deploy the AWI war file as downloaded from Automic (do not just copy the war file to the webapps folder - yes, it kind of works, but you can't undeploy cleanly for example; use the management web interface instead)
5. create the neccessary config files from the ".sample" files - as far as essentials go, this mostly comes down to webapp/config/uc4config.xml, where you configure your AE connection, and configuration.properties, where you define the URL for the web help to be used.
6. stop and restart the AWI web app once after changing the config, using the management interface
Best,
Carsten