Python: understanding class and instance variables

You are running into initialization issues based around mutability.

First, the fix. skills and energy are class attributes. It is a good practice to consider them as read only, as initial values for instance attributes. The classic way to build your class is:

class Animal(object):
    energy = 10
    skills = []
    def __init__(self,en=energy,sk=None):
        self.energy = en
        self.skills = [] if sk is None else sk 

   ....

Then each instance will have its own attributes, all your problems will disappear.

Second, what's happening with this code? Why is skills shared, when energy is per-instance?

The -= operator is subtle. it is for in-place assignation if possible. The difference here is that list types are mutable so in-place modification often occurs:

In [6]: 
   b=[]
   print(b,id(b))
   b+=['strong']
   print(b,id(b))

[] 201781512
['strong'] 201781512

So a1.skills and a2.skills are the same list, which is also accessible as Animal.skills. But energy is a non-mutable int, so modification is impossible. In this case a new int object is created, so each instance manages its own copy of the energy variable:

In [7]: 
     a=10
     print(a,id(a))
     a-=1
     print(a,id(a))

10 1360251232
9 1360251200

Access the class variables through the class, not through self:

class Animal(object):
    energy = 10
    skills = []

    def work(self):
        print 'I do something'
        self.__class__.energy -= 1

    def new_skill(self, skill):
        self.__class__.skills.append(skill)

Upon initial creation both attributes are the same object:

>>> a1 = Animal()
>>> a2 = Animal()
>>> a1.energy is a2.energy
True
>>> a1.skills is a2.skills
True
>>> a1 is a2
False

When you assign to a class attribute, it is made local to the instance:

>>> id(a1.energy)
31346816
>>> id(a2.energy)
31346816
>>> a1.work()
I do something
>>> id(a1.energy)
31346840  # id changes as attribute is made local to instance
>>> id(a2.energy)
31346816

The new_skill() method does not assign a new value to the skills array, but rather it appends which modifies the list in place.

If you were to manually add a skill, then the skills list would be come local to the instance:

>>> id(a1.skills)
140668681481032
>>> a1.skills = ['sit', 'jump']
>>> id(a1.skills)
140668681617704
>>> id(a2.skills)
140668681481032
>>> a1.skills
['sit', 'jump']
>>> a2.skills
['bark', 'sleep']

Finally, if you were to delete the instance attribute a1.skills, the reference would revert back to the class attribute:

>>> a1.skills
['sit', 'jump']
>>> del a1.skills
>>> a1.skills
['bark', 'sleep']
>>> id(a1.skills)
140668681481032

The trick here is in understanding what self.energy -= 1 does. It's really two expressions; one getting the value of self.energy - 1, and one assigning that back to self.energy.

But the thing that's confusing you is that the references are not interpreted the same way on both sides of that assignment. When Python is told to get self.energy, it tries to find that attribute on the instance, fails, and falls back to the class attribute. However, when it assigns to self.energy, it will always assign to an instance attribute, even though that hadn't previously existed.