<p>I cloned a Git master and made a lot of changes on the clone. I have since committed these changes on the clone and now want the master to be a carbon copy of what is on the clone.</p>

<p>I've tried Git push on the clone to push the changes to the master - but nothing I do updates the master.</p>

<p>How can I make the master an exact copy of what is on the clone? What is the command workflow of updating the clone and having the master sync with the clone?</p>

There are 2 kinds of git repository, bare and non-bare. A non bare repository is any repository which has a 'working copy' i.e. some part of the repository currently checked out.
You
can
push into a non-bare repository, but it won't update the checked out working copy even if the checked out branch is the same as the branch you pushed. This is because the checked out copy might have changes that aren't committed, and git won't ever destroy changes without you explicitly asking (usually such commands have a --hard argument)
Read
Why won't I see changes in the remote repo after "git push"?
and
How would I use "git push" to sync out of a firewalled host?
for a full description of the problem and a potential solution. Word of warning, if you've pushed into a remote repo, any non-committed changes in that remote-repo will have to be discarded.
Generally it sounds like the approach you want isn't really adopted by gitters, because it doesn't really match the distributed repository mentality. It's your own responsibility to make sure your copy of the repo is up to date.