This page has general notes on installing JIRA on Tomcat 5.5.x. It supplements the official Tomcat installation docs.
A user writes:
There is a readme file shipped with JIRA. It said that you need to change port 8080 in order to get Tomcat(say a) to start up. BUT, if you have a CATALINA_HOME environment variable already set for an existing Tomcat(say b) running on the same server, running startup from the bin directory will start up Tomcat(b). For Tomcat(a) to start one needs to delete the existing CATALINA_HOME environment variable as well.