Below are the shortest steps I know that would get you the smallest Java web application ready in Maven.
$ mkdir -p webapp/src/main/webapp/WEB-INF/classes
$ echo '<web-app></web-app>' > webapp/src/main/webapp/WEB-INF/web.xml
$ echo '<html>Hello World.</html>' > webapp/src/main/webapp/index.jsp
$ echo '<project>
</project>' > webapp/pom.xml
$ cd webapp
$ mvn org.apache.tomcat.maven:tomcat7-maven-plugin:2.0-beta-1:run
You should able to visit http://localhost:8080/webapp after that. Editing any JSP files should auto refresh by the server, and you don't need to restart it. This is a fast way to prototype and test out your ideas.
(Yes, I am aware that maven has the archetype for webapp, but it above do give you the bare minimal and you see each lines what go into your project.)