If your components are defined in code rather than fxml you will currently (with JavaFX 2.2) need to create the infrastructure yourself.
Quick algorithm off the top of my head:
1. assign an id to each labeled or text node (setId).
2. use the text key strings in your resource bundle which match your node id.
3. create a resourcebundle property on your scene.
4. attach a resourcebundle property ChangeListener.
5. when the resourcebundle for the scene changes:
a. iterate through all your text keys from the resource bundle.
b. invoke the node.lookup(textKeyId) function for each text key.
c. call node.setText(rb.getString(textKeyId)).
If you use fxml, see here for info on how to hook up resources:
http://docs.oracle.com/javafx/2/api/javafx/fxml/doc-files/introduction_to_fxml.html#resource_resolution
If you use SceneBuilder, follow this guide to internationalize your app:
http://docs.oracle.com/javafx/scenebuilder/1/user_guide/i18n-support.htm
Also, see the example in this stackoverflow question (also an fxml variant):
http://stackoverflow.com/questions/10143392/javafx-2-and-internationalization