$other_database = array(
      'database' => 'databasename',
      'username' => 'username', // assuming this is necessary
      'password' => 'password', // assuming this is necessary
      'host' => 'localhost', // assumes localhost
      'driver' => 'mysql', // replace with your database driver
  );
  // replace 'YourDatabaseKey' with something that's unique to your module
  Database::addConnectionInfo('YourDatabaseKey', 'default', $other_database);
  db_set_active('YourDatabaseKey');

  // execute queries here

  db_set_active(); // without the paramater means set back to the default for the site
  drupal_set_message(t('The queries have been made.'));