I set up a small web project with JSF and maven. Now I want to deploy on a Tomcat Server.
During development I recommend to use Eclipse Web Tools Platform (WTP). M2Eclipse provides support for it (assuming you have Maven Integration for WTP installed) and your project should be recognized as a Dynamic Web Project runnable on a Server.
So, declare Tomcat as a Server (show the Servers view and right-click in it to add a Server via New > Server). And deploy your project to it (right-click on your project then Run > Run on Server).
There are other options like using the Tomcat Maven Plugin
or the generic Cargo Maven Plugin
but I wouldn't use them for development and, since you are a Maven beginner, I don't recommend them at all. Use your IDE.
I read about a the Maven War Plugin but I couldn't find a tutorial how to integrate that into my process.
Actually, the Maven War Plugin is only responsible of the packaging of your webapp project (it is bound automatically on the package
phase when using a <packaging>war<packaging>
for your project). It isn't used for deployment. But as I said, use your IDE to deploy your application during development.