This isn't really specific to Alfresco or Tomcat. You'll need an entry in your DNS server that maps your domain to the IP address of your tomcat server. Tomcat listens for requests on port 8080. If you don't want people to have to specify the port in the URL, you'll either need to configure it to listen on port 80 (not recommended), use a port forwarding setup on your machine to forward requests that come in on port 80 to port 8080, or configure apache to handle the requests and forward on to tomcat. This last option is the most prevalent.
To implement the last option, you want something called the Apache Tomcat Connector, which is often referred to as mod_jk. There is a page on the Alfresco wiki that explains how to set this up. But, as I said, this is common to everyone who uses the Apache web server with Tomcat, so you should be able to find lots of resources about it on the web.
