What is the bare minimum setup of a private cloud looks like. Is there a blue print ?
That is a bit like asking how long a piece of string is. It depends on what you want to tie down. What are the requirements you need, and why are you wanting a private cloud are questions that need to be answered first I think. There is a start here: https://azure.microsoft.com/en-au/overview/what-is-a-private-cloud/