How does inheritance of __slots__ in subclasses actually work?

As others have mentioned, the sole reason for defining __slots__ is to save some memory, when you have simple objects with a predefined set of attributes and don't want each to carry around a dictionary. This is meaningful only for classes of which you plan to have many instances, of course.

The savings may not be immediately obvious -- consider...:

>>> class NoSlots(object): pass
... 
>>> n = NoSlots()
>>> class WithSlots(object): __slots__ = 'a', 'b', 'c'
... 
>>> w = WithSlots()
>>> n.a = n.b = n.c = 23
>>> w.a = w.b = w.c = 23
>>> sys.getsizeof(n)
32
>>> sys.getsizeof(w)
36

From this, it would seem the with-slots size is larger than the no-slots size! But that's a mistake, because sys.getsizeof doesn't consider "object contents" such as the dictionary:

>>> sys.getsizeof(n.__dict__)
140

Since the dict alone takes 140 bytes, clearly the "32 bytes" object n is alleged to take are not considering all that's involved in each instance. You can do a better job with third-party extensions such as pympler:

>>> import pympler.asizeof
>>> pympler.asizeof.asizeof(w)
96
>>> pympler.asizeof.asizeof(n)
288

This shows much more clearly the memory footprint that's saved by __slots__: for a simple object such as this case, it's a bit less than 200 bytes, almost 2/3 of the object's overall footprint. Now, since these days a megabyte more or less doesn't really matter all that much to most applications, this also tells you that __slots__ is not worth the bother if you're going to have just a few thousand instances around at a time -- however, for millions of instances, it sure does make a very important difference. You can also get a microscopic speedup (partly due to better cache use for small objects with __slots__):

$ python -mtimeit -s'class S(object): __slots__="x","y"' -s's=S(); s.x=s.y=23' 's.x'
10000000 loops, best of 3: 0.37 usec per loop
$ python -mtimeit -s'class S(object): pass' -s's=S(); s.x=s.y=23' 's.x'
1000000 loops, best of 3: 0.604 usec per loop
$ python -mtimeit -s'class S(object): __slots__="x","y"' -s's=S(); s.x=s.y=23' 's.x=45'
1000000 loops, best of 3: 0.28 usec per loop
$ python -mtimeit -s'class S(object): pass' -s's=S(); s.x=s.y=23' 's.x=45'
1000000 loops, best of 3: 0.332 usec per loop

but this is somewhat dependent on Python version (these are the numbers I measure repeatably with 2.5; with 2.6, I see a larger relative advantage to __slots__ for setting an attribute, but none at all, indeed a tiny disadvantage, for getting it).

Now, regarding inheritance: for an instance to be dict-less, all classes up its inheritance chain must also have dict-less instances. Classes with dict-less instances are those which define __slots__, plus most built-in types (built-in types whose instances have dicts are those on whose instances you can set arbitrary attributes, such as functions). Overlaps in slot names are not forbidden, but they're useless and waste some memory, since slots are inherited:

>>> class A(object): __slots__='a'
... 
>>> class AB(A): __slots__='b'
... 
>>> ab=AB()
>>> ab.a = ab.b = 23
>>> 

as you see, you can set attribute a on an AB instance -- AB itself only defines slot b, but it inherits slot a from A. Repeating the inherited slot isn't forbidden:

>>> class ABRed(A): __slots__='a','b'
... 
>>> abr=ABRed()
>>> abr.a = abr.b = 23

but does waste a little memory:

>>> pympler.asizeof.asizeof(ab)
88
>>> pympler.asizeof.asizeof(abr)
96

so there's really no reason to do it.

class WithSlots(object):
    __slots__ = "a_slot"

class NoSlots(object):       # This class has __dict__
    pass

First Item

class A(NoSlots):            # even though A has __slots__, it inherits __dict__
    __slots__ = "a_slot"     # from NoSlots, therefore __slots__ has no effect

Sixth Item

class B(WithSlots):          # This class has no __dict__
    __slots__ = "some_slot"

class C(WithSlots):          # This class has __dict__, because it doesn't
    pass                     # specify __slots__ even though the superclass does.

You probably won't need to use __slots__ in the near future. It's only intended to save memory at the cost of some flexibility. Unless you have tens of thousands of objects it won't matter.