What is the general function to add a Widget area (not of a particular type)?

Adding on mikesars answer, afterwards, one needs to Place the widget in a template file like header.php (for example).

So it would be:

functions.php:

if ( function_exists('register_sidebar') )
  register_sidebar(array(
    'name' => 'Name of Widgetized Area',
    'before_widget' => '<div class = "widgetizedArea">',
    'after_widget' => '</div>',
    'before_title' => '<h3>',
    'after_title' => '</h3>',
  )
);

Template file:

<?php if ( !function_exists('dynamic_sidebar') || 
!dynamic_sidebar("Widgetized Area") ) : ?>
<?php endif;?>