How does a holographic object change perspective when the image is rotated? Fundamentally I want to know: How do holograms work?
The problem with that question is that normally you will end up with pages and pages talking about:


*

*a laser

*a beam splitter

*a diffuser

*the object being imaged

*object beam

*reference beam

*mirror

*holographic emulsion


Even Wikipedia is heavy on how to make a hologram, rather than how does a hologram work.

Other people have mentioned stereoscopic vision; how having two eyes gives the illusion of a 3d object. That is also irrelavent, since someone with one eye (or, in my case, one eye closed) can still experience a hologram.
What I am trying to figure out is how does a hologram work?. More to the point, how is it that rotating a flat holographic sticker allows the virtual object to change orientation - allowing me to see content that was not there a moment ago?

Wikipedia has an image that mentions reconstructing a virtual 3d object:

Some problems that that image, though, is that my credit card:


*

*has no reference beam

*is not being viewed at a 45 degree angle (meaning no interference can happen)


Assuming I have a holographic image of a simple cube. If I am looking at the holographic plate straight on, I will only see a square (i.e. the face of the cube closest to me):

If i rotate the holographic plate, so the right side of the plate is further away, the virtual cube will rotate, and I will actually be able to see the left face of the cube:

What is happening in the flat, 2-dimensional, holographic sticker that it can display continuously different information as I rotate it?
What is the mechanics of this holographic "paper" that it can present my eye different images?
 A: 
What i am trying to figure out is how does a hologram work?. More to the point, how is it that rotating a flat holographic sticker allows the virtual object to change orientation - allowing me to see content that was not there a moment ago?

You see objects because your eyes register light that is coming from these objects. If you shift your head, your eyes will be subjected to a different "part" of reflected light waves from those objects, so you will see those objects differently -- for example you will be able to see objects that was obscured before. 
Suppose that you have a techique that records completely all the light waves coming from your objects. And you also can "playback" those waves, so that they would exaclty reproduce the lightwaves from real objects. Then no one will be able to distinguish (using only one's eyes) the difference between the real objects and your "lightwave reproduction" of them. If you shift your head, your eyes will be subjected to a different "part" of "reproduced" light waves, so you will "see" those "objects" differently -- for example you will be able to "see objects" that was "obscured" before. 
That is roughly what holograms do. They record the whole information about the incoming light by storing it in the interference patterns in a film. And when hologrms reflect (or, sometimes, pass through) light they reproduce exactly the lightwaves that was falling on them during recording.

...my credit card: 
  
  
*
  
*has no reference beam
  
*is not being viewed at a 45 degree angle (meaning no interference can happen)
  

Well, first about interference. I think you misunderstand what does "interference" mean in that context. We are talking about wave interference between object wave and reference wave. The hologram records interference pattern, that is produced by wave interference of the two waves. And all that is relevant during creation of a hologram.  
The interference patterns are very fine -- they are of a size of a wavelength. So there is a lot of information recorded on the hologram -- that is how all that information "fits" on one hologram.
Finally. When we reconstruct a hologram we use a reference beam, which diffracts on the recorded interference patterns and reproduces the object wave. 
Now, speaking about reference beam. First of all -- you always need "reference beams" to see something. Light have to come from somwhere to get into your eye, right? On the other hand, for basic old-style holograms it is actually necessary to use a laser beam to recreate recorded waves. But there is a more "modern" approach called volume holograms, which work in ordinary light.
