How to extract PDF fields from a filled out form in Python?

You should be able to do it with pdfminer, but it will require some delving into the internals of pdfminer and some knowledge about the pdf format (wrt forms of course, but also about pdf's internal structures like "dictionaries" and "indirect objects").

This example might help you on your way (I think it will work only on simple cases, with no nested fields etc...)

import sys
from pdfminer.pdfparser import PDFParser
from pdfminer.pdfdocument import PDFDocument
from pdfminer.pdftypes import resolve1

filename = sys.argv[1]
fp = open(filename, 'rb')

parser = PDFParser(fp)
doc = PDFDocument(parser)
fields = resolve1(doc.catalog['AcroForm'])['Fields']
for i in fields:
    field = resolve1(i)
    name, value = field.get('T'), field.get('V')
    print '{0}: {1}'.format(name, value)

EDIT: forgot to mention: if you need to provide a password, pass it to doc.initialize()

Python 3.6+:

pip install PyPDF2

# -*- coding: utf-8 -*-

from collections import OrderedDict
from PyPDF2 import PdfFileWriter, PdfFileReader


def _getFields(obj, tree=None, retval=None, fileobj=None):
    """
    Extracts field data if this PDF contains interactive form fields.
    The *tree* and *retval* parameters are for recursive use.

    :param fileobj: A file object (usually a text file) to write
        a report to on all interactive form fields found.
    :return: A dictionary where each key is a field name, and each
        value is a :class:`Field<PyPDF2.generic.Field>` object. By
        default, the mapping name is used for keys.
    :rtype: dict, or ``None`` if form data could not be located.
    """
    fieldAttributes = {'/FT': 'Field Type', '/Parent': 'Parent', '/T': 'Field Name', '/TU': 'Alternate Field Name',
                       '/TM': 'Mapping Name', '/Ff': 'Field Flags', '/V': 'Value', '/DV': 'Default Value'}
    if retval is None:
        retval = OrderedDict()
        catalog = obj.trailer["/Root"]
        # get the AcroForm tree
        if "/AcroForm" in catalog:
            tree = catalog["/AcroForm"]
        else:
            return None
    if tree is None:
        return retval

    obj._checkKids(tree, retval, fileobj)
    for attr in fieldAttributes:
        if attr in tree:
            # Tree is a field
            obj._buildField(tree, retval, fileobj, fieldAttributes)
            break

    if "/Fields" in tree:
        fields = tree["/Fields"]
        for f in fields:
            field = f.getObject()
            obj._buildField(field, retval, fileobj, fieldAttributes)

    return retval


def get_form_fields(infile):
    infile = PdfFileReader(open(infile, 'rb'))
    fields = _getFields(infile)
    return OrderedDict((k, v.get('/V', '')) for k, v in fields.items())



if __name__ == '__main__':
    from pprint import pprint

    pdf_file_name = 'FormExample.pdf'

    pprint(get_form_fields(pdf_file_name))