Try something like this:
<link rel="stylesheet" href="<?php bloginfo('stylesheet_directory'); ?>/page.css" type="text/css" media="screen" />
If you want to use the same header.php as the other templates, you’ll probably need to modify it to do something like this:
<?php if (is_page()): ?>
<link rel="stylesheet" href="<?php bloginfo('stylesheet_directory'); ?>/page.css" type="text/css" media="screen" />
<?php else ?>
<link rel="stylesheet" href="<?php bloginfo('stylesheet_url'); ?>" type="text/css" media="screen" />
<?php endif; ?>
If you want custom stylesheets for several differnet pages, you’ll need something like such:
if (is_page('about-page')):
// do stuff
else if (is_page('links-page')):
// do stuff
...
else:
// default stuff
endif;
is_page() can accept a page id, a page name, or a sanitized URI-safe version of the page name.