I'd like to be able to add tags to my pages just like I can with posts.
What would I need to do to enable the tag editor/entry for the page editor?
You can use the register_taxonomy_for_object_type
function.
The following adds the default 'tag' and 'category' taxonomies to pages:
register_taxonomy_for_object_type('post_tag', 'page');
register_taxonomy_for_object_type('category', 'page');