First, decide what size your finished puzzle will be, that is, what unit cube size to use. I would suggest 15mm since this is a nice size to play with and does not take up too much room in your puzzle collection. Obviously the smaller the pieces the more problems you will have with tolerances. If you lack confidence - make it bigger!

Next prepare a supply of "stick". Or, have your friendly local craftsman supply it. It MUST be finished accurately to size and perfectly square.
Assuming a unit size of 15mm, you will need approx. 1.5metres for pieces A - H and 200mm in a contrasting species of wood for the Calf this will allow plenty for waste and saw kerf.

Cut the stick to length - you need 2 length 4; 14 length 3; 2 length 2; 10 length 1 for E-H, and 4 length 2 for the Calf.
Now construct the pieces as per the diagram. Note the position of the end grain. Building the pieces in this way helps to prevent distortion due to climate change since the wood will expand/contract in the same direction. The adhesive that I use is Franklin's Titebond (the Moulding version) this is an aliphatic resin glue and is "fast grab". The fast grab nature of this adhesive means that little clamping is required. It has also proved highly durable and your joints are less prone to "popping" than with other types.
All that remains is for you to give a finish to your pieces and to construct a box to store them in.