Thank you for that info, Steve.
I think
http://androidscript.org/ide/ should just say, "Open DroidScript on your phone, tap the WiFi icon, and follow the instructions." That's it. Otherwise, the instructions conflict and are confusing. BTW, even entering the IP address and port number of my phone in that form gave me the very same Connection error message.
At any rate, I've found out why the app won't run. The Debug tab was helpful (thank you) in that it showed me the click on the Run button was indeed recognized by the IDE. The content in that tab totally cleared when I clicked the button, but showed no errors, or anything FTM, whatsoever.
Thinking it might be a firewall issue, even though it should not be, I fired up Wireshark and captured the packets between my desktop and the phone. I see the IDE sending the Run command: GET /ide?cmd=run&prog=MyFirstApp&_=1618076876934 HTTP/1.1
The response is:
HTTP/1.1 500 No virtual method getSystemService(Ljava/lang/Class;)Ljava/lang/Object; in class Landroid/content/Context; or its super classes (declaration of 'android.content.Context' appears in /system/framework/framework.jar)
The IDE does not catch and inform of that error.
Now, since DroidScript was not on the Play Store, I have no idea what the system requirements are. I am running Android 5.1.