How does a Python set([]) check if two objects are equal? What methods does an object need to define to customise this?

Yes, you need a __hash__()-method AND the comparing-operator which you already provided.

class Item(object):
    def __init__(self, foo, bar):
        self.foo = foo
        self.bar = bar
    def __repr__(self):
        return "Item(%s, %s)" % (self.foo, self.bar)
    def __eq__(self, other):
        if isinstance(other, Item):
            return ((self.foo == other.foo) and (self.bar == other.bar))
        else:
            return False
    def __ne__(self, other):
        return (not self.__eq__(other))
    def __hash__(self):
        return hash(self.__repr__())