python __init__ method in inherited class

Just call the parent's __init__ using super:

class inheritedclass(initialclass):
    def __new__(self):
        self.attr3 = 'three'
        super(initialclass, self).__init__()

I strongly advise to follow Python's naming conventions and start a class with a Capital letter, e.g. InheritedClass and InitialClass. This helps quickly distinguish classes from methods and variables.

First of all you're mixing __init__ and __new__, they are different things. __new__ doesn't take instance (self) as argument, it takes class (cls). As for the main part of your question, what you have to do is use super to invoke superclass' __init__.

Your code should look like this:

class initialclass(object):
    def __init__(self):
        self.attr1 = 'one'
        self.attr2 = 'two'    

class inheritedclass(initialclass):
    def __init__(self):
        self.attr3 = 'three'
        super(inheritedclass, self).__init__()

It's incredibly simple. Define a new __init__ method and call the parent's __init__ at the beginning.

# assuming a class Base, its __init__ takes one parameter x

class Derived(Base):
    def __init__(self, x, y):
        # whatever initialization is needed so we can say Derived is-a Base
        super(Derived, self).__init__(x)
        # now, add whatever makes Derived special - do your own initialization
        self.y = y

In Python 3, you don't have to (and therefore propably shouldn't, for simplicity) explicitly inherit from object or pass the class and self to super.

As far as I know that's not possible, however you can call the init method of the superclass, like this:

class inheritedclass(initialclass):
    def __init__(self):
        initialclass.__init__(self)
        self.attr3 = 'three'