How do I customize the search result page?
You can override theme_search_results(), or theme_search_result().

The first is the theme function that is invoked for the search result page, while the second is the theme function that is invoked to render a single result. Both the theme functions use a template file (search-results.tpl.php in the first case, search-result.tpl.php in the second case).

search-result.tpl.php would use $info_split['type'] in Drupal 6, which contains the node type. In the latest Drupal 7 version, $info_split['type'] is not anymore passed, but search-result.tpl.php still gets $result['node'], in the case the search is done for nodes; $result['node']-&gt;type is then the content type of the node.

To notice that Drupal 7, and higher, allows the modules to implement hook_search_page(), but it is a hook used by a module that integrates with the Search module, not from a module that wants to change the result page for results returned by another module.
Also, on Drupal 7, each theme function uses a preprocess function, which in this case would be hook_preprocess_search_results() and hook_preprocess_search_result(). They are helpful in the case you just need to edit the value of what passed to the template file.