How we get the success messages

You can declare $success variable and use it to display success message as following.

Declare $success variable and assign success message to it if user is registered successfully as following :

$success="";
if ( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) && $_POST['action'] == 'adduser' ) {
$user_pass = wp_generate_password();
$userdata = array(
    'user_login' => esc_attr( $_POST['user_name'] ),
    'user_pass' => esc_attr( $_POST['pass1'] ),
    'user_email' => esc_attr( $_POST['email'] ),
    'user_url' => esc_attr( $_POST['website'] ),
    'description' => esc_attr( $_POST['description'] ),
    'role' => get_option( 'default_role' ),
);

if ( !$userdata['user_login'] )
    $error = __('A username is required for registration.', 'frontendprofile');
elseif ( username_exists($userdata['user_login']) )
    $error = __('Sorry, that username already exists!', 'frontendprofile');

elseif ( !is_email($userdata['user_email'], true) )
    $error = __('You must enter a valid email address.', 'frontendprofile');
elseif ( email_exists($userdata['user_email']) )
    $error = __('Sorry, that email address is already used!', 'frontendprofile');
else if ( $_POST['pass1'] !== $_POST['pass2'] ) {
    $error = __('Sorry, Passwords must match', 'frontendprofile');
}
else if ( strlen( $_POST['pass1'] ) < 6 ) {
    $error = __('Sorry, Passwords must be at least six characters long', 'frontendprofile');
}
else{
    $new_user = wp_insert_user( $userdata );
 if (!is_wp_error($return) ){
    $success = __($userdata['user_login'].' User registered $userdata['user_login'].', 'frontendprofile');
    wp_new_user_notification($new_user, $user_pass);
}
}
}

And you can use that $success variable to display message as following:

if($success)
     echo $success;

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