If you read further in the document you linked it looks like there's no one standard style:

Optional keyword parameters have default values, which are displayed as part of the function signature. They can also be detailed in the description:

Description of parameter `x` (the default is -1, which implies summation
over all axes).

When a parameter can only assume one of a fixed set of values, those values can be listed in braces, with the default appearing first:

order : {'C', 'F', 'A'}
    Description of `order`.

I would recommending picking a style for your own project and sticking to it.

Formats

Python docstrings can be written following several formats as the other posts showed. However the default Sphinx docstring format was not mentioned and is based on reStructuredText (reST). You can get some information about the main formats in this blog post.

Note that the reST is recommended by the PEP 287

There follows the main used formats for docstrings.

- Epytext

Historically a javadoc like style was prevalent, so it was taken as a base for Epydoc (with the called Epytext format) to generate documentation.

Example:

"""
This is a javadoc style.

@param param1: this is a first param
@param param2: this is a second param
@return: this is a description of what is returned
@raise keyError: raises an exception
"""

- reST

Nowadays, the probably more prevalent format is the reStructuredText (reST) format that is used by Sphinx to generate documentation. Note: it is used by default in JetBrains PyCharm (type triple quotes after defining a method and hit enter). It is also used by default as output format in Pyment.

Example:

"""
This is a reST style.

:param param1: this is a first param
:param param2: this is a second param
:returns: this is a description of what is returned
:raises keyError: raises an exception
"""

- Google

Google has their own format that is often used. It also can be interpreted by Sphinx (ie. using Napoleon plugin).

Example:

"""
This is an example of Google style.

Args:
    param1: This is the first param.
    param2: This is a second param.

Returns:
    This is a description of what is returned.

Raises:
    KeyError: Raises an exception.
"""

Even more examples

- Numpydoc

Note that Numpy recommend to follow their own numpydoc based on Google format and usable by Sphinx.

"""
My numpydoc description of a kind
of very exhautive numpydoc format docstring.

Parameters
----------
first : array_like
    the 1st param name `first`
second :
    the 2nd param
third : {'value', 'other'}, optional
    the 3rd param, by default 'value'

Returns
-------
string
    a value in a string

Raises
------
KeyError
    when a key error
OtherError
    when an other error
"""

Converting/Generating

It is possible to use a tool like Pyment to automatically generate docstrings to a Python project not yet documented, or to convert existing docstrings (can be mixing several formats) from a format to an other one.

Note: The examples are taken from the Pyment documentation