Classes as well as their instances in python uses dictionary like data structure to store the information.

So for each class definition, a dictionary will be allocated where the class level information (class variables) will be stored. And for each instance of that particular class, a separate dictionary(self) will be allocated where the instance specific information(instance variables) will be stored.

So now the next question is: How the lookup for a particular name will be performed ??

And answer to this question is that if you are accessing the names through some instance, the instance specific dictionary will be searched first and if the name is not found there, then the class dictionary will be searched for that name. So if the same value is defined at both levels that former one will be overridden.

Note that when you write d['key'] = val where d is a dictionary, 'key' will automatically be added to the dictionary if not already present. Otherwise the current value will be overwritten. Keep this in mind before reading the further explanation.

Now lets go through the code you have used to describe your problem:

MyClass1

class MyClass1:
    q=1
    def __init__(self,p):
        self.p=p
    def AddSomething(self,x):
        self.q = self.q+x

1. my = Myclass1(2) #create new instance and add variables to it.

    MyClass = {"q" : 1}
    my = {"p" : 2}

2. my.p    # =2, p will be taken from Dictionary of my-instance.

3. my.q    # =1, q will be takn from MyClass dict. (Not present in dictionary of my-instance).

4. my.AddSomething(7) # This method access the value of q (using self.q) first 
                      # which is not defined in my dict and hence will be taken
                      # from dictionary of MyClass. After the addition operation,
                      # the sum is being stored in self.q. Note that now we are
                      # adding the name q to Dictionary of my-instance and hence                   
                      # a new memory space will be created in Dictionary of my-instance
                      # and the future references to self.q will fetch the value
                      # of self.q from dictionary of my-instance.

    MyClass = {"q" : 1}
    my = {"p" : 2, "q" : 8}

5. my.q   # =8, q now is available in dictionary of my-instance.

Try the inspect module. getmembers and the various tests should be helpful.

EDIT:

For example,

class MyClass(object):
    a = '12'
    b = '34'
    def myfunc(self):
        return self.a

>>> import inspect
>>> inspect.getmembers(MyClass, lambda a:not(inspect.isroutine(a)))
[('__class__', type),
 ('__dict__',
  <dictproxy {'__dict__': <attribute '__dict__' of 'MyClass' objects>,
   '__doc__': None,
   '__module__': '__main__',
   '__weakref__': <attribute '__weakref__' of 'MyClass' objects>,
   'a': '34',
   'b': '12',
   'myfunc': <function __main__.myfunc>}>),
 ('__doc__', None),
 ('__module__', '__main__'),
 ('__weakref__', <attribute '__weakref__' of 'MyClass' objects>),
 ('a', '34'),
 ('b', '12')]

Now, the special methods and attributes get on my nerves- those can be dealt with in a number of ways, the easiest of which is just to filter based on name.

>>> attributes = inspect.getmembers(MyClass, lambda a:not(inspect.isroutine(a)))
>>> [a for a in attributes if not(a[0].startswith('__') and a[0].endswith('__'))]
[('a', '34'), ('b', '12')]

...and the more complicated of which can include special attribute name checks or even metaclasses ;)