Given the following code snippet, how would you create a Jasmine spyOn test to confirm that doSomething gets called when you run MyFunction
        
When you call new MyCoolObject() you invoke the MyCoolObject function and get a new object with the related prototype. This means that when you spyOn(MyCoolObject, "doSomething") you're not setting up a spy on the object returned by the new call, but on a possible doSomething function on the MyCoolObject function itself.
You should be able to do something like:
it("calls doSomething", function() {
  var originalConstructor = MyCoolObject,
      spiedObj;
  spyOn(window, 'MyCoolObject').and.callFake(function() {
    spiedObj = new originalConstructor();
    spyOn(spiedObj, 'doSomething');
    return spiedObj;
  });
  MyFunction();
  expect(spiedObj.doSomething).toHaveBeenCalled();
});
Alternatively, as Gregg hinted, we could work with 'prototype'. That is, instead of spying on MyCoolObject directly, we can spy on MyCoolObject.prototype.
describe("MyFunction", function () {
    it("calls doSomething", function () {
        spyOn(MyCoolObject.prototype, "doSomething");
        MyFunction();
        expect(MyCoolObject.prototype.doSomething).toHaveBeenCalled();
    });
});