In Drupal 6 I would go to the taxonomy section of my /admin and I'd be able to find the $vid (numerical) in the URL.
In Drupal 7 (no doubt due to the introduction of terms as entities) the URL is no longer as verbose (and some would say cleaner) as it now shows the machine name (bundle name?) of the vocabulary as it can be seen in
My end-game is to use taxonomy_get_tree($vid, $parent, $max_depth, $load_entities) to load my vocabulary, and work with it in glorious and plentiful ways, but alas this function does not accept a machine_name but presumably prefers the numerical
I'll accept alternatives to load a full vocab tree (i.e. all terms and their relationships to each other), but I do think that this question should be answered directly for future generations to google.