Move code examples out from docs

[rytilahti]

Code examples could be moved out from the docs to make them easier for library users to find, and we can add some tests to keep them working in the future.

..literalinclude can be used to show them inside the docs.

I think we should probably "externalize" these examples into regular .py files to allow testing them, as I'm worried about documentation rot over time. This can be done in a separate PR at some later point though, so just make sure the example script is working for now.

Originally posted by @rytilahti in #614 (comment)