I am using eclipse Indigo, In project explorer I can see my project there. I want to add server to my project so that I can run/test my web application.
After creating new server of type Tomcat > Tomcat 6. A window appear to add/move resource (my project) to right window so that new server configured with my project. But that window is empty. How I can show my project in left window?

following Project Facets installed

You have to be absolutely sure that your project has Web Project Facet enabled. You can enable facets in project properties. Normally the facet you are looking for is called Dynamic Web Module.