Here is the sample for JavaFX dialog. There is no dialog api in JavaFx 2.x. So you have create your own stage and create components in it.
import javafx.application.Application;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.Label;
import javafx.scene.layout.HBox;
import javafx.scene.layout.StackPane;
import javafx.scene.layout.VBox;
import javafx.stage.Modality;
import javafx.stage.Stage;
/**
 * @author JayaPrasad
 * 
 */
public class SampleDialog extends Application {
    /*
     * (non-Javadoc)
     * 
     * @see javafx.application.Application#start(javafx.stage.Stage)
     */
    @Override
    public void start(Stage primaryStage) throws Exception {
        primaryStage.setTitle("JavaFx Dialog");
        Button btn = new Button();
        btn.setText("Click me to display popup dialog");
        btn.setOnAction(new EventHandler<ActionEvent>() {
            @Override
            public void handle(ActionEvent event) {
                final Stage dialogStage = new Stage();
                dialogStage.initModality(Modality.WINDOW_MODAL);
                Label exitLabel = new Label("Are you sure you want to exit?");
                exitLabel.setAlignment(Pos.BASELINE_CENTER);
                Button yesBtn = new Button("Yes");
                yesBtn.setOnAction(new EventHandler<ActionEvent>() {
                    @Override
                    public void handle(ActionEvent arg0) {
                        dialogStage.close();
                    }
                });
                Button noBtn = new Button("No");
                noBtn.setOnAction(new EventHandler<ActionEvent>() {
                    @Override
                    public void handle(ActionEvent arg0) {
                        dialogStage.close();
                    }
                });
                HBox hBox = new HBox();
                hBox.setAlignment(Pos.BASELINE_CENTER);
                hBox.setSpacing(40.0);
                hBox.getChildren().addAll(yesBtn, noBtn);
                VBox vBox = new VBox();
                vBox.setSpacing(40.0);
                vBox.getChildren().addAll(exitLabel, hBox);
                dialogStage.setScene(new Scene(vBox));
                dialogStage.show();
            }
        });
        StackPane root = new StackPane();
        root.getChildren().add(btn);
        primaryStage.setScene(new Scene(root, 300, 250));
        primaryStage.show();
    }
    public static void main(String[] args) {
        launch(args);
    }
}