How do I add something to the breadcrumb?

You can use the add() method to add a crumb:

\Aero\Store\Facades\Breadcrumb::add(function (\Aero\Store\Services\Breadcrumb $breadcrumb) {
    $breadcrumb->add(new \Aero\Store\Crumb('Name', '/url'));
});

You can provide a Closure that returns an \Aero\Store\Crumb instance instead if you need to defer until the breadcrumb is rendered.