How to send e-mails

Using the Mail::send() method

The Mail core class extends ObjectModel

This example is assuming you are using in a controller named mycontroller of a module named mymodule

class mymodulemycontrollerModuleFrontController extends ModuleFrontController
{

    public function initContent()
    {
        parent::initContent();
        Mail::Send(
            (int)(Configuration::get('PS_LANG_DEFAULT')), // defaut language id
            'contact', // email template file to be use
            ' Module Installation', // email subject
            array(
                '{email}' => Configuration::get('PS_SHOP_EMAIL'), // sender email address
                '{message}' => 'Hello world' // email content
            ),
            Configuration::get('PS_SHOP_EMAIL'), // receiver email address 
            NULL, //receiver name
            NULL, //from email address
            NULL  //from name
        );
    }
}

Prestashop will use the Shop Configuration to decide if use smtp connection or php mail function so check it out on backoffice or in app/config/parameter.php