You can install the SSH & Web Terminal add-on through Hassio that will allow you to SSH into the container.
I have that addon installedā¦ but the issue is that just ssh into the internal ip address listed in the network details for addon_40817795_nut (172.30.33.1) results in a connection refused. The ip address of the base system is 192.168.1.6. I was able to assign a different ssh port to the base Ubuntu system and have ssh access now to the base system via port 2222 and to the hassio terminal via port 22. But the nut container does not list an option to assign a port to it.
I would not be caught dead without that addon, saved my butt many times in the early days of learning hassio on the Pi! 
You can execute one-line commands in the container like so:
docker exec container_name whatever command args you like
@FredTheFrog, that works amazingly well. Thanks for the info, I really am reading and learningā¦ not just asking here. Just a little overwhelmed at the moment with all the changes after years of running on a pi only.