I'm trying to add a block to the sidebar which contains a currency exchange widget.  I made the block and called it "currency-rates." Next I copied and pasted code from a currency exchange widget into the content portion of the block:

Then I went to the home page of my site and expanded the sidebar tool and dragged the Pages => Custom Blocks thing into the right sidebar. I edited it, and selected "currency-rates." The I clicked "Finish Editing." But all I get is this:

That's it. No currency rates displayed. I also tried this with a few other currency exchange widgets and had the same problem, there's just a link and again, no currency exchange data.

How can I create a block with an external widget, and display it in my sidebar?

The procedure is correct. I tested it on both my IPS sites. It worked on my http site without problems. 

It failed on my https site though, because the non-secure script writing content to the browser is probably blocked. Not sure if that is also the problem for you, but it’s very likely a JavaScript-related problem with these widgets. 

Yep, pretty much hit the nail on the head there....

• if your site is http only, then that code you provide is going to work.
• If your site is https, then that code is going to fail because of mixed content (http/https) and the browser will block it.
• https://fx-rate.net times out, so you can't change the http to https in the html code

Best option: contact fx-rate.net and ask about them providing https service.