if (!defined('_PS_VERSION_'))
  exit;

<?php
if (!defined('_PS_VERSION_'))
  exit;

class MyModule extends Module
{
  public function __construct()
  {
    $this->name = 'mymodule';
    $this->tab = 'Test';
    $this->version = 1.0;
    $this->author = 'Firstname Lastname';
    $this->need_instance = 0;

    parent::__construct();

    $this->displayName = $this->l('My module');
    $this->description = $this->l('Description of my module.');
  }

  public function install()
  {
    return parent::install();
  }
}
?>

public function __construct()

$this->name = 'mymodule';
$this->tab = 'Test';
$this->version = 1.0;
$this->author = 'PrestaShop';

$this->need_instance = 0;

parent::__construct();

$this->displayName = $this->l('My module');

$this->description = $this->l('Description of my module.');

public function install()
{
  return (parent::install());
}

// this also works, and is more future-proof
public function install()
{
  if (parent::install() == false)
    return false;
  return true;
}

If your module does create SQL data, whether in its own MySQL tables or in the XXXX table, then it should also feature an uninstall() method, so as to have a custom uninstallation process. This method could look like so:

public function uninstall()
{
  if (!parent::uninstall())
    Db::getInstance()->Execute('DELETE FROM `'._DB_PREFIX_.'mymodule`');
  parent::uninstall();
}

public function install()
{
  if (parent::install() == false OR !$this->registerHook('leftColumn'))
    return false;
  return true;
}

// then...

public function hookLeftColumn( $params )
{
  global $smarty;
  return $this->display(__FILE__, 'mymodule.tpl');
}

public function hookRightColumn($params)
{
  return $this->hookLeftColumn($params);
}

if (parent::install() == false OR !$this->registerHook('leftColumn'))
  return false;
return true;

public function hookLeftColumn($params)
{
  global $smarty;
  return $this->display(__FILE__, 'mymodule.tpl');
}

public function hookRightColumn($params)
{
  return $this->hookLeftColumn($params);
}

<!-- Block mymodule -->
<div id="mymodule_block_left" class="block">
  <h4>Welcome!</h4>
  <div class="block_content">
    <ul>
      <li><a href="{$base_dir}modules/mymodule/mymodule_page.php" title="Click this link">Click me!</a></li>
    </ul>
  </div>
</div>
<!-- /Block mymodule -->

Welcome to my shop!

<?php
global $smarty;

include('../../config/config.inc.php');
include('../../header.php');

$mymodule = new MyModule();
$message = $mymodule->l('Welcome to my shop!');
$smarty->assign('messageSmarty', $message); // creation of our variable
$smarty->display(dirname(__FILE__).'/mymodule_page.tpl');

include( '../../footer.php' );
?>

{$messageSmarty}

{debug}

{* This string is commented out *}

{*
This string is too!
*}

...
$this->displayName = $this->l('My module');
$this->description = $this->l('Description of my module.');
...

<li>
  <a href="{$base_dir}modules/mymodule/mymodule_page.php" title="Click this link">Click me!</a>
</li>

<li>
  <a href="{$base_dir}modules/mymodule/mymodule_page.php" title="{l s='Click this link' mod='mymodule'}">{l s='Click me!' mod='mymodule'}</a>
</li>

<h4>Welcome!</h4>
...
Click me!

<h4>{l s='Welcome!' mod='mymodule'}</h4>
...
{l s='Click me!' mod='mymodule'}

<?php

global $_MODULE;
$_MODULE = array();
$_MODULE['<{mymodule}prestashop>mymodule_b268021027834ab9a4fe675f0c0a93ef'] = 'Mon module';
$_MODULE['<{mymodule}prestashop>mymodule_8dc6964360034754105d1328b04d7727'] = 'Description de mon module';
$_MODULE['<{mymodule}prestashop>mymodule_19d8055bcd0e60a5f99c807e50094c4e'] = 'Cliquez sur ce lien';
$_MODULE['<{mymodule}prestashop>mymodule_526fdd5deb77218de6497b4f3f5b5c65'] = 'Cliquez-moi \!';
$_MODULE['<{mymodule}prestashop>mymodule_page_9cfb297375a799e0f130804c089bd034'] = 'Bienvenue dans ma boutique \!';

<?php
class Test extends ObjectModel 
{
  /** @var string Name */
  public $test;

  protected $fieldsRequired = array('test');
  protected $fieldsSize = array('test' => 64);
  protected $fieldsValidate = array('test' => 'isGenericName');
  protected $table = 'test';
  protected $identifier = 'id_test';

  public function getFields() 
  {
    parent::validateFields();
    $fields['test'] = pSQL($this->test);
    return $fields;
  }
}
?>

<?php
include_once(PS_ADMIN_DIR.'/../classes/AdminTab.php');

class AdminTest extends AdminTab
{
  public function __construct()
  {
    $this->table = 'test';
    $this->className = 'Test';
    $this->lang = false;
    $this->edit = true;
    $this->delete = true;
    $this->fieldsDisplay = array(
      'id_test' => array(
        'title' => $this->l('ID'),
        'align' => 'center',
        'width' => 25),
      'test' => array(
        'title' => $this->l('Name'),
        'width' => 200)
    );

    $this->identifier = 'id_test';

    parent::__construct();
  }

  public function displayForm()
  {
    global $currentIndex;

    $defaultLanguage = intval(Configuration::get('PS_LANG_DEFAULT'));
    $languages = Language::getLanguages();
    $obj = $this->loadObject(true);

    echo '
      <script type="text/javascript">
        id_language = Number('.$defaultLanguage.');
      </script>';

    echo '
      <form action="' . $currentIndex . '&submitAdd' . $this->table . '=1&token=' . $this->token . '" method="post" class="width3">
        '.( $obj->id ? '<input type="hidden" name="id_'.$this->table.'" value="'.$obj->id.'" />' : '' ).'
        <fieldset><legend><img src="../img/admin/profiles.png" />'.$this->l('Profiles').'</legend>
          <label>'.$this->l('Name:').'</label>
          <div class="margin-form">';

    foreach ($languages as $language)
      echo '
          <div id="name_'.$language['id_lang'|'id_lang'].'" style="display: '.($language['id_lang'|'id_lang'] == $defaultLanguage ? 'block' : 'none').'; float: left;">
            <input size="33" type="text" name="name_'.$language['id_lang'|'id_lang'].'" value="'.htmlentities($this->getFieldValue($obj, 'name', intval($language['id_lang'|'id_lang'])), ENT_COMPAT, 'UTF-8').'" /><sup>*</sup>
          </div>';

    $this->displayFlags($languages, $defaultLanguage, 'name', 'name' );
    echo '
          <div class="clear"></div>
        </div>
        <div class="margin-form">
          <input type="submit" value="'.$this->l('Save').'" name="submitAdd'.$this->table.'" class="button" />
        </div>
        <div class="small"><sup>*</sup> '.$this->l('Required field').'</div>
      </fieldset>
    </form> ';
  }
}
?>