Back in the olden days of 2006 / 2007, it was easy. Install # Stop Tomcat (so it isn't running). Grab the # .WAR file and drop it into the proper directory within Tomcat. Start Tomcat. Once it has extracted the WAR file, stop Tomcat again and edit some configs (for example, enter database info, enable or disable various services and functionality). Start it again.

Depending on what gets enabled, there could be other shutdowns and restarts and config editing needed.