This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Use Tomcat standalone on port 80. You need to make sure nothing else is binding to port 80 if you do this (e.g. Apache).
Using Apache as a front-end you can use it as a proxy with mod_proxy or mod_proxy_ajp to pass through requests on port 80 to the Tomcat listening port. This requires configuration changes to Apache, and possibly installation of the modules. This is what your question implies you are looking for.
Alternatively you can use mod_jk to allow Apache to treat Tomcat as a sort of CGI handler for any content you specify. In this case you'll need to build and install a mod_jk module for your Apache installation and configure both Apache and Tomcat to use mod_jk.
There are pros and cons to each approach. The biggest issues I can think of are security, performance, and future upgrades (e.g. load balancing on multiple servers) You'll have to research these if you consider them important.
Documentation for each option is available at apache.org.