This will extract the search query from a Google search. It doesn't specifically look for Google in the referer so it may capture more than just Google searches. You can use this information to re-perform the search on your own site or just keep it for your own records.

$referer = $_SERVER[HTTP_REFERER];

if($referer)
{
    preg_match("/[\&\?]q=([^&]*)/", $referer, $matches);

    if($matches[1])
    {
        $search_query = rawurldecode($matches[1]);
        $search_query = str_replace("+", " ", $search_query);
    }
}

print "You searched Google for '$search_query'";