Best How To :

You're doing it wrong

First thing is that PHP4-style constructors are deprecated, use __construct method to define a costructor.

Second is that you must not return from constructor but rather keep the connection object inside class as instance property.

Third is that you must call parent methods using parent keyword.

class Mysql
{
    const SERVER, USER, PASSWORD, DB;

    protected $conn;

    function __construct()
    {
        $this->conn = mysqli_connect(self::SERVER, ETC);
    }
}

class Mysql_Select extends Mysql
{
    function __construct()
    {
        parent::__construct();
        // use $this->conn here from the parent class.
    } 
}