This is about the most basic Singleton you can make. It uses a class method to check whether the singleton has been created and makes a new one if it hasn't. There are more advanced ways of going about this, such as overriding the __new__ method.

class Singleton:
    instance = None
    
    @classmethod
    def get(cls):
        if cls.instance is None:
            cls.instance = cls()
        return cls.instance
    
    def __init__(self):
        self.x = 5       # or whatever you want to do

sing = Singleton.get()
print sing.x  # prints 5

This is about the most basic Singleton you can make. It uses a class method to check whether the singleton has been created and makes a new one if it hasn't. There are more advanced ways of going about this, such as overriding the __new__ method.

class Singleton:
    instance = None
    
    @classmethod
    def get(cls):
        if cls.instance is None:
            cls.instance = cls()
        return cls.instance
    
    def __init__(self):
        self.x = 5       # or whatever you want to do

sing = Singleton.get()
print sing.x  # prints 5

As for why your code fails, there are several reasons. First, by the time __init__ is called, a new object has already been created, defeating the purpose of the singleton pattern. Second, when you say self = __instance, that simply resets the local variable self; this would be akin to saying

def f(x):
  x = 7    # changes the value of our local variable

y = 5
f(y)
print y   # this is still 5

Since variables in Python are passed by value and not reference, you can't say self = blah and have it be meaningful in the way you want. The above Singleton class is more what you want, unless you want to get fancy and look into overriding the __new__ operator.