You should indeed start creating a plugin (File->New->Plugin project)
Then, you have to define extensions to tell Eclipse to add the desired button and associated action.
Double click on the manifest.mf file to define new extensions (Extensions tab).
Check org.eclipse.ui plugin is added to your plugin dependencies (Dependencies tab).
You can use org.eclipse.ui.menus (to define the location of your button or menu) and org.eclipse.ui.commands extension points (to define the command and the associated handler that will run your application).
Export your plugin (File->Export) and install it in your Eclipse/plugins folder.
Restart Eclipse, your plugin should be taken in account
Note that the jar defining your application should be embedded in your plugin and be part of the plugin runtime classpath.