We can help you in this forum with styling the search box, but for in-depth advice on setting up the form, you’d need something like the CMS forum. Basically, though, if you want to use the WP search functionality, presumably you first have to go into your files (sidebar.php?) and move the search form code up into the “container” div.
Or you could ditch the WP form altogether and go for a Google search form, as Eric suggested.