From http://tomcat.apache.org you can download a ZIP file, unzip it, run startup.bat in bin directory and you will have Tomcat up and running. I covered this in previous tutorial. This is great for testing and development and you should definitelly try it, but in production there's a more useful approach, which is running Tomcat as a Windows service.
First download Tomcat Windows Service installer and run it. During installation you can define ports and create a user, which will be able to access a Manager application. You must also select a path to Java. And finally a destination folder where will be Tomcat installed.
The only difference between this Tomcat and a Tomcat from a ZIP file is inside a bin directory, where are no startup and shutdown scripts, but there are two executable files. First one starts a Tomcat and the second one is an application used for Tomcat startup configuration.