I still do not get if ethereum creators want it to be single blockchain or not? If not, where are instructions for creating my own blockchain to play with?
Ethereum offers a platform for anyone to create their own applications which are powered by the blockchain technology. Just like Bitcoin, Ethereum also has a public blockchain. So, you can either run your application on the public blockchain, or you can start your own blockchain.
Here are some useful links that'll help you create your own blockchain: