Tomcat is simply a web server/servlet container. Which means that is it is capable of accepting and processing http requests. However, you only need to go through the trouble of configuring Tomcat once, then your web server is up and running.
In general, most of your work on a website will be developing the application itself, which would then be deployed in your the $TOMCAT_HOME/webapps directory as a .war file. Tomcat knows how to handle it from there.
As far as application development is concerned, I recommend looking into the Spring Framework. It's unquestionably one of the industry standards, and with annotation configuration you'll be up and running quite quickly.
There are a ton of blog posts detailing how to use Spring annotations. For getting of the ground, I recommend this good, if somewhat dated, tutorial. It doesn't use annotations, but it walks you through setting up your first website using Spring, Tomcat, JSP, and a database.