Two things: first, change Tomcat to listen to port 80 instead of port 8080. Since port 80 is the default for HTTP requests, it is not necessary to specify it. Open your server.xml file and search for "8080".
Second, you need to register a domain name with a company like GoDaddy or Network Solutions. They will associate your domain name with the IP address of the server your site is hosted on. If you don't have a public, static IP address, you'll either need to get one or find a hosting company to host your site.