How do I obtain a list of categories assigned to the current post?

You can use get_the_category()

It will return an array of category IDs belonging to the current post.

$post_cats= array();
$categories = get_the_category();
foreach($categories as $cat) :
array_push($post_cats, $cat->cat_id);
endforeach;

Then the $post_cats array will have a list of all the ids.