Q:

Best method for creating shape using anchor points

Here is an image that I drew by hand. I am looking for a way
to create precise distances between anchors (blue dots) and a way to
connect them with straight lines (black).
I have photoshop and illustrator. Can someone please provide
a clear list of steps to take in either of these programs?
Ideally I would like to be able to fill some of the parts with colour. 

I basically want the A's and B's to be equal. 

Ideally I use a grid to position my points for shape corners.
Like this: 

But this is an online generator
(http://tommaitland.net/graphpaper/)
and I need to do this in photoshop or illustrator. 

A:

Most likely, the result must be an extruded profile (or parallel projection). Of course we wouldn't use the extrude tool in Illustrator.
All you have to do is to draw your profile (the B's) and copy it to give the extrusion effect you want the extrusion amount will be (the A's).
This Projection called Axonometric projection where it is a type of parallel projection used for creating a pictorial drawing of an object, where the object is rotated along one or more of its axes relative to the plane of projection.
Considering that you have a equiangular please follow my steps.

you have two option to draw a equiangular, one using the polygon tool and the other way is to draw with line segments explained by @joojaa
you should have a profile shape like the one below.

select the shape and copy it in a new diagonal direction.

with the line tool, connect all the pointed angles.

A:

Use illustrator its by far easier. After your edits its easier to understand what your after. Basically your asking if there is a grid snap? Sure, to turn the grid on and turn grid snapping on:

Choose View → Show Grid
Then enable gridsnapping View → Snap to Grid

the rest  should be self explanatory on account that you know how to draw the shape. But to add a bit your shape is a parallelogram. That means that you can always clone the opposite side by alt dragging selected shape to clone path parts. 
Now its not so easy to do this on a grid. As the length of edges does not necessarily coincide with the grid (especially when your at an angle). When you hold Alt and click then you get a dialog for entering values for the tool. This will help you doing the drawing WITHOUT a grid. Just type in direction and line length and then clone them around.

Image 1: Time lapse of a arbitrary example
Tip: Use the line tool its conceptual easier. If you need the shape closed afterwards just use shape builder tool to make shapes.

