Search redirects to site home page

By default, the search results are sent to the homepage… you can customize the search results by creating a search.php page, but this is NOT the search results page, it’s simply a way to customize how the search results work. If you want a special page to show the search results, you’ll need to create a template. These directions will show you exactly what you need. It covers all options.

http://codex.wordpress.org/Creating_a_Search_Page