Ubercart 2.x: Given a product nid, retrieve its manufacturer
In Drupal 6 taxonomy terms are linked to the node object, Ubercart just piggy-backs off the way Drupal core handles this.

You can use the very handy taxonomy_node_get_terms_by_vocabulary() function to grab all of the terms associated with a node in a certain vocabulary. You would use it like so:

$vid = 1; // Vocabulary ID
$nid = 1; // Node ID

$node = node_load($nid);
$terms = taxonomy_node_get_terms_by_vocabulary($node, $vid);