Drupal 7 now uses php data objects (PDO). The configuration file sites/default/settings.php now has lots of fanciness to support the variety of ways that it's possible to connect to a variety of databases.
If you're on XAMPP and you get a PDO:_construct error, I'll bet it's the unix socket. Here's the fix. Locate the section that specifies your database, username, and password, and add a 'unix_socket' line like below.
$databases = array (
'database' => 'database_name',