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A private cloud is a cloud computing platform built on your own hardware and software. The alternative is to deploy the services you need on a public cloud infrastructure provided by an external supplier such as Amazon Web Services, Rackspace Cloud or HP Public Cloud. While a public cloud can afford greater flexibility, with all resource delivered as a service and billed by the hour, a private cloud gives you the advantage of greater control over the entire stack, from the bare metal up to the services accessible to users.
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Here is another guide that might be helpful is you are going the ubuntu path:
Here's how a guy from RightScale says he built a private cloud in his garage.
I know you don't expect "step by step," but this writer outlines five steps to building a private cloud.
This presentation from an O'Reilly OSCON conference details how to build a private cloud with Ubuntu Server 10.04 Enterprise Cloud.
Not sure about the minimal requirements, but this article goes into a lot of detail about building a private cloud lab environment. It might help give you an idea.