There is no common dialog support. .....
do yourself...
Stage dialogStage = new Stage();
dialogStage.initModality(Modality.WINDOW_MODAL);
dialogStage.setScene(new Scene(VBoxBuilder.create().
children(new Text("Hi"), new Button("Ok.")).
alignment(Pos.CENTER).padding(new Insets(5)).build()));
dialogStage.show();
・controlsfx? jdk8からサーポート
・javafx-dialogs-0.0.3.jar 使える、かなり便利!