Microsoft Word 2013 will not download templates.

Exactly what do you mean "download templates"?

Please describe the steps you are taking in detail so we can try to recreate your problem.

Great, you are getting an error message. SO WHAT IS IT!?! We need the FULL and EXACT error message text so we can provide specific suggestions.

Wow!

Okay, exactly what happens is, I go into Microsoft word, I want to open a new document, it gives me template choices, I choose a template, I get to the "Create Template" screen, error message reading, "Something went wrong when downloading your template."

That's it. 

I have also read the responses to the same question as posed by others, and they have had no joy in it being answered, which includes a link for updates that apparently does not work.

OK, that makes sense.  Just to confirm, you want to create a new file (aka "open a new document") using the provided templates displayed by the "File menu > New command"?

What is happening is that in 2013, MS assumes that everyone has high speed internet connections all the time. So rather than giving you a copy to all of the templates that are displayed, it simply shows you a "thumbnail" preview of it and gives you an internet link to download it.  For some reason your downloads are failing.

Exactly which templates are you trying?  We can try them to, to confirm if they are really still available.  When you first click on a template it displays more information. At the top of the information is the source. Who is providing the templates you are having problems with? Most likely MS, but they do have links to other companies too ...

Sorry, I have not encountered that specific error message.

As a workaround, try going direct to the internet. In your browser, enter this address:

http://office.microsoft.com/

Then click on the word "Templates" at the top of the page.  Search for your desired templates and try downloading from there.

Bizarrely, I just opened the template named "Basic Resume" and it worked.  It was a Microsoft Corporation template, so I will look at others and see if it was due to them being from other sources.  I just tried the template search and it now also seems to be working. 

I cannot imagine what has changed except the year...literally. 

Thank you for your links, I will bookmark those so in the future if I have repeat issues I can use them.

If the only thing that has changed is the year, you must be on the other side of the world (I still have 4.5 hours to go ... ).

I suspect that the problem was either at the MS servers that you were directed to.