I have an Orchard CMS test site running in Azure. I have some theme files I want to deploy to the site. How do I do that? I was made a co-admin using my live-ID by the way.
It depends do you want a temporarily put something to the server or is the change something that needs to be there after some publishes new version to the Azure.
If remote desktop is enabled then you can put some css files temporarily there (those will disappear after publishing new version as there will be new instance of virtual machine). Also if you have multiple instances of virtual machines then you have to copy the files to each of them. I don't recommend this solution.
If you want changes to be always there then you need to add theme files to your project and publish a new version. There are lots of instructions how to publish new version to the Azure (for example this one).
There might be some Orchard specific solutions that I am not aware of, these instructions are about Azure in general.