Take a look at the $_GET and $_REQUEST superglobals. Something like the following would work for your example:
$start = $_GET['start'];
$limit = $_GET['limit'];
EDIT
According to this post in the laravel forums, you need to use Input::get()
, e.g.,
$start = Input::get('start');
$limit = Input::get('limit');
See also: http://laravel.com/docs/input#input