You'd need something like this (to be added in functions.php):
add_action('wp_enqueue_scripts','wpse57014_register_script');
function wpse57014_register_script(){
//Register and enqueue stylesheet only on this page
if ( is_page( 'mypage' ) ) {
wp_register_style( 'wpse57014_mypage_stylesheet', get_template_directory_uri().'/mypage-style.css' );
wp_enqueue_style( 'wpse57014_mypage_stylesheet' );
}
}
Where mypage is the slug of the page on which ONLY you want to load the stylesheet. Replace instances of mypage in the code to keep the code understandable to you (or modify it as you wish, if you know what you are doing).
get_template_directory_uri().'/mypage-style.css' is the path to the stylesheet in your theme, for example — http://example.com/wp-content/themes/MY THEME/mypage-style.css.
conditional tags to edit css— that's not very clear. But you can have a CSS file load only on a specific page, if that's what you wantbody_class()in the body tag (in header.php ?) ?