This is really easy to do in cpanel. What I didn't know: www.mysite.com/rg and rg.mysite.com are equivalent
There are two different ways to do this. I did it in multiple steps, but it would have been easier to do it one step (more later). I created a folder (rg) from my main web, and then right clicked on it *in the folder view*, and selected "Convert to web". I did this with an empty folder--if you already have files in the web, you can still create the subweb, but links from/to them might be corrupted.
Just double click on it. You can't "work with" a childweb (subweb) in the main web window. It won't let you view the files.
Same as always--this part was the easy part.
I thought I should publish to rg.mysite.com--but it wouldn't accept my password. What it wanted was to publish to www.mysite.com/rg. Remember--those two are logically the same. It published to www.mysite.com/rg without a problem, *and* it could be viewed by rg.mysite.com.
You set the protections using the "server" option on the Tools menu. However, if you are editing your web on your hard disk (which is what most of us do, and is usually the best way to build your website), that option isn't available. It is *only* available if you open the *actual* web on the server.
a) To open your web on the Paravel Solutions server: Go to Open Web on the Files menu, and enter the top level web address. I think but am not positive that I had to use http://www.mysite.com/rg. Once I got that set up, http://rg.mysites.com worked also, but I don't think it worked the first time.
Set permissions for this subweb: you need them to be *different* from the parent web
c) Manage users. I think the main user is automatically set (but can't repeat it to be sure). Create at least one additional user with a username or password, and assign a role (how much stuff they can do). That's the username/password you'll give to other people.
d) Change "anonymous access settings"--you need to disable anonymous access settings so that a password is *required* to even get to the top page of your subweb.