How to display "message sent" after to invoke commandButton ?

See my code xhtml:

My class Java:

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
package com.incoreside.Newsletter;

import java.awt.event.ActionEvent;
import javax.faces.bean.ManagedBean;
import javax.faces.bean.RequestScoped;

/**
 *
 * @author hackum
 */
import javax.faces.application.FacesMessage;
import javax.faces.context.FacesContext;
@ManagedBean(name = "newsletterBean")
@RequestScoped
public class Newsletter {

/**
     * Creates a new instance of Newsletter
     */
    
    private String nome;
    private String email;
    String message = "Enviado com sucesso!";    
    public Newsletter() {
    }
    
    public void setNome(String nome)
    {
        this.nome = nome;
    }
    
    public String getNome()
    {
        return nome;
    }
    
    public void setEmail(String email)
    {
        this.email = email;
    }
    
    public String getEmail()
    {
        return email;
    }

public void execute()
    {
        System.out.print("it worked! " + nome);
       
    }
    
    public void displayMessage(ActionEvent actionEvent)
    {
       
        FacesContext.getCurrentInstance().addMessage(null, new FacesMessage("it worked! " + nome + " " + email + "!"));
    }
}

it not worked!

You're doing a full page submit which is why the message doesn't appear, but something like this should do what you want
(note that you're specifying null as the id in addMessage() so you need h:messages, to get the h:message components to
render you need to give them ids and include them in the render= attribute value of the f:ajax tag):

Regards,
Brendan.