Here's the answer:
1. Get somehow to the overview page. There's a list of property setup functions on the right side.
2. Fiddle with the "Template" options if you must, but what is really needed is to click "Layout". This takes you to a page that displays the layout as movable widgets in the places that they appear on the page.
3. Click the "Edit" link for the widget to be deleted, in this case "Blog Archive" which lists posts by date. Wait a few seconds for a window to pop up with configuration options. Down at the bottom of this configuration window is a button labeled "Remove". Click this and tell it that yes you really want to.
4. Click any "Add a Gadget" link in the layout. Wait a few seconds for a window to pop up. This lists all the "Gadgets," none of which look like any of the ordinary features we are trying to work with. However, way down at the bottom of the list are the more mundane page element, including the one that we want which in this case is the boringly named "Labels" widget. The main issue here was that for Blogger these are not called tags, they're called "Labels".
5. Now a widget box appears on the layout. Move and stretch it until it's in the proper location. Click the Edit button to set up parameters. Click "Save Configuration" to exit.
The breakthroughs that were so hard to get to via Google's help pages is that these things are called "Page Elements", and the tag list is found under the name "Labels" in the "Gadget List."
Here's the first, terribly unhelpful link from helpblogger which concerned itself with directly editing obscure tags in the HTML. It turns out that this was not at all necessary for what I was trying to do, but is interesting anyhow:
http://helplogger.blogspot.com/2012/03/hideshow-widgetsgadgets-in.html
Here's a hilariously shallow description of labels, without any information about how to display them on the blog page. However at this point we have the first key, to look for terminology "label" instead of "tag":
https://support.google.com/blogger/answer/44498?hl=en
Here's a page that states what I am trying to do (add labels as a page element) but doesn't actually go into detail about how to do it. I probably should have tried the links at the bottom of the page.
http://www.blogsbyheather.com/2008/08/blogger-using-c.html
This hint looks like the current setup but is only minimally related to my quest:
http://123techguide.blogspot.com/2012/01/add-page-element-to-blogger.html#axzz2tX6MLs8C
This page wasn't too helpful, but this is where I realized that the "gadget" list now contains "Page Elements" as well and I finally figured out that the element I needed was there all along:
https://support.google.com/blogger/answer/43708?hl=en#survey=true
