Looks like the first line contains a short description (should not exceed one line, as described in PEP 257), that will be put after the name; followed by a blank line and then a paragraph, what will be used to provide content in the DESCRIPTION section.
So, for instance if you have this in just_to_see/__init__.py (simple example with a module):
"""A short description
A longer description on several lines etc.
blablabla etc."""
def a_function():
"""
An interesting introductive comment.
Some more explanations.
"""
pass
(note that the doc string can be elsewhere, like in a __doc__ attribute, as stated here)
then pydoc3.4 just_to_see/__init__.py will output:
Help on module __init__:
NAME
__init__ - A short description
DESCRIPTION
A longer description on several lines etc.
blablabla etc.
FUNCTIONS
a_function()
An interesting introductive comment.
Some more explanations.
FILE
/home/nico/temp/just_to_see/__init__.py
If your package is installed (in a virtual environment for instance), some more informations can be found by pydoc from its setup.py (like author's name etc.).
Not sure about how to trigger an EXAMPLES section. Couldn't find any example of an EXAMPLE section in the pydoc output of a standard python library yet (but I haven't browsed them all). Maybe you can add such a section in the long description in the doc string of your package. But as they don't seem to do it in the standard libraries, maybe it's not the right place to put examples?