I created a stable branch of my code in my local git repository.  Then
I pushed it up to the GitHub server.  So, I can see it in my local
repository and on the remote server, however, when I do a new clone of
my repository and execute the "git branch" command, only the mast
branch shows up.  What have I done wrong?

And by "mast branch", I mean "master branch"... typo.

Ahhh, I got it.  I found a tech note that talks about how to checkout
another branch from a remote repository.  Here it is, in case this is
helpful to anyone else:

$ git clone http://www.example.com/~username/git/repo-name
$ cd repo-name
$ git fetch
$ git checkout --track -b mybranch origin/remote-branch-name

Ah, the classic case of finding your answer just after you give up and send
off an email.

git-clone should pull down all the remote branches, you shouldn't need that
fetch call.  After it pulls those down, however, it creates only a local
branch named "master"... so you have to create any other local branches you
want.

--tek