(First of all, many thanks to the support and assistance provided by this community).
Here is the solution to the original question:
- If you have a "free public account" for ArcGIS Online, you're out of luck. You can't export. I'm using a Learn ArcGIS account, which works. You may need to request a higher "role" from your organization's administrator to get access to the Publish and Export functions needed here.
- In your ArcGIS online map, create a layer called Map Notes from the drop-down menu.
- Add points and lines to your map as you wish. (Personally, no luck exporting Text or Areas.)
- Save your map.
- Save the Map Notes layer by clicking on the three dots for the layer (last item).
- Under the home arrow (top left of map screen) select "Content".
- Click on the Map Notes item in the Content window
- Click on the Publish button
- In the resulting window, click on the Export button, and choose the format you wish. I'm using KML (warning: ArcGIS actually exports KMZ rather than KML.)
- Download the file. If you chose KML or CSV, you'll get a .zip file which when unzipped gives you four files for each type of data: points, lines, areas, text.
- Import the files into whatever program you're using. Warning: the lines and points have no elevation data in them so you'll need to apply that in the program you're using.
I think that's it.
If someone more knowledgable about the workings of this forum than I can change this post to the "accepted solution" I think that would help others find this info in the future. @Anonymous User you might be able to do this as the author of the current "accepted solution".
Sincerely,
Ken