How can I learn about how cloning works in nature (twins)?
To learn about the process of how cloning works, you need to appreciate the underlying principles. A general bio textbook should suffice (most popular one is Alberts, where you should focus on chapter 21, but maybe read other chapters for background)

Nature Scitable is also a good source.

I'd discourage reading research papers at this stage, primary research paper are often very specialized, and reviews are aimed at other researchers in the field, that is unless you find one that is focused on communicating science to the public.