HTML :

<fieldset>
<legend><h2>Se connecter pour plus de contenu</h2></legend>

<form method="POST" action ="page2.php">
<input type="mail" name ="id" placeholder="Identifiant"><br/>
<input type="password" name="mdp" placeholder="Mot de passe"/><br/>
<input type="submit" name="valide" value="Valider" />
</form>

</fieldset>

PHP :

<?php
  if(isset($_POST['valide']) && $_POST['valide'] == 'Valider')
  {
    if(isset($_POST['id']) && trim(htmlspecialchars($_POST['id'])) != null && isset($_POST['mdp']) && trim(htmlspecialchars($_POST['mdp'] == '1234')))
    {
      echo 'Connexion réussie';
      if(!session_start())
      {
        session_start();
      }
      $_SESSION['bonobo']['email'] = $_POST['id'];
    }
    else if(isset($_POST['mdp']) && $_POST['mdp'] != '1234')
    {
      echo 'Mauvais mot de passe';
    }
  }

  if(isset($_SESSION['bonobo']['email']))
  {
    ?>
    <h1>Bonjour à tous blabla ... </h1>
    <?php
  }
?>