To run MultiChain on Azure, simply follow the instructions here:
http://www.multichain.com/download-install/
There's also a one-click 'Deploy to Azure' link there, though the manual installation process for MultiChain is very easy.
Once you have it up and running I recommend going through this tutorial:
http://www.multichain.com/download-install/
That covers all of the actions you're asking about.