Measuring The Distance To Very Distant Quazars and the like

I would really like to know how the Astronomers use "Red Shift", in the light spectrum,
to determine the distance to a very distant objects (see title).

The way I understand what the astronomers are doing is:

1. gather the light from a very distant object.
2. Pass the gathered light through a prism
3. Measure how far the red light has shifted. The more it shifts the farther away it is.

If this is where they stop their calculation of distance, to the very distant object , I feel
their calculations are only 1/2 to 3/4 finished.

I'll explain my reasoning and I will use numbers for distance and speed that make the math
much easier. You could use the actual distance and speed numbers and it would make no
real difference but you would need a calculator.

So...the numbers I will use are......10 billion lightyears to the very distant object and it is
moving away from us at 1Mph under the speed of light. Basically the speed of light.

This is how I see it.

1. Light leaves the very distant object 10 billion years ago on its trip to Earth and the
    very distant object is  traveling in the opposite direction at the speed of light.

2. 10 billion years later the light finally reaches Earth but also the very distant object has
    traveled at the speed of light for 10 billion years in the opposite direction.

3. In reality the very distant object is 20 billion light years away from us (right now) but
    Astronomers can't see the very distant object at 20 billion lightyears because the light
    from it hasn't reached us yet. It will though in 10 billion years

This make me wonder if the Universe is expanding, contracting or what. There is a large
gap in what the Astronomers are seeing and what is actually happening out there right
now. Possibly billions of years gap.

Whacha Tink

Peace