I used my scaled up drawing as a reference when cutting the different layers of my blank.
Individual slices of wood were cut using the wood shop's bandsaw, and, after each cut, I sanded the rough sawn edges down smoothly using the disk sander in our shop.
I used 4 different types of scrap wood from a bunch of previous projects to make my blank. Redheart for the rocket cap, maple for the white body, mahogany for the accent line, and walnut for the booster. (The mahogany and the walnut were too similar in color, so they didn't delineate very well in the finished product.) It was pretty important that I kept all of the wood grains aligned for a spindle blank, rather than a bowl blank. This means that all of the wood grains ran parallel to the intended axis of rotation for the blank.
Using a liberal amount of wood glue, I glued and clamped each layer one by one, giving each layer 30 minutes to cure before I added on a new layer. After gluing all of the layers together, I let the whole thing set overnight.