1. Make Java 1.5 the default JRE
2. Get the core distribution from http://tomcat.apache.org/ At the time of this writing that would be: apache-tomcat-6.0.13.tar.gz
3. Unpacking will create a apache-tomcat-6.0.13 folder, probably on your desktop. Move this folder into /usr/local, like this:
   
   sudo mv ~/Desktop/apache-tomcat-6.0.13 /usr/local
4. To make it easy to replace this release with future releases, we are going to create a symbolic link that we are going to use when revering to Tomcat:
   
   sudo ln -s /usr/local/apache-tomcat-6.0.13 /Library/Tomcat
5. Next step is making Tomcat's launch and stop scripts executable:
   chmod ug+x /Library/Tomcat/bin/*.sh
6. Create startup and shutdown scripts:
   Startup:
   Open TextEdit and create a startTomcat.command file in your home folder ...
   
   #!/bin/sh # -------------------------------------------------- # Start Script for the Tomcat Server # -------------------------------------------------- export CATALINA_HOME=/Library/Tomcat export JAVA_HOME=/Library/Java/Home $CATALINA_HOME/bin/startup.sh
   
   Shutdown:
   Open TextEdit and create a stopTomcat.command file in your home folder ...
   
   #!/bin/sh # --------------------------------------------------- # Start Script for the Tomcat Server # --------------------------------------------------- export CATALINA_HOME=/Library/Tomcat export JAVA_HOME=/Library/Java/Home $CATALINA_HOME/bin/shutdown.sh
   
   
7. Open a Terminal and make both scripts executable:
   
   • chmod ug+x ~/startTomcat.command
   • chmod ug+x ~/stopTomcat.command
8. Change ownership of the /Libaray/Tomcat folder hierarchy:
   
   sudo chown -R your_username /Library/Tomcat
9. Start Tomcat by simply clicking the startTomcat.command icon in your home folder.
   Test with http://localhost:8080

Instead of using the start and stop scripts, you may also want to check out activata's Tomcat Controller a tiny freeware app, providing a UI to quickly start/stop Tomcat.