Be sure that Tomcat is stopped first before adding it in Eclipse. You do not need to start or stop Tomcat outside Eclipse because you can do it inside Eclipse.
You may be forgetting to fill up the Server name textbox. Next button will be ungreyed once you filled up that textbox.
Upon clicking Next you need to specify the Tomcat installation directory (if you downloaded a binary) as highlighted in the Tomcat installation directory textbox. You can also click Download and install button if you don't have Tomcat yet or if you just want to be sure of that you want have the right version.
You can either click Next or Finish. Click Next to add a previous project to Tomcat. Otherwise click Finish to return to your current perspective.
After returning to your perspective, just in case you are not in Java EE perspective, do this: From the menu bar click Window -> Open Perspective -> Other -> Java EE. As you can see at the bottom I have selected the Servers tab and my newly created Tomcat server is already there and was stopped. You can start or stop this server by right clicking it.