Paperweight designing

I'm guessing that because you are asking the question, you do not have any power tools.

If I were making this, I would use my circular bench saw/bandsaw and planer.

But there is no reason that you could not use a simple handsaw to produce the two basic shapes.

I would rough cut the two shapes in contrasting timbers, plane or sand one edge square and smooth so that they mated closely. They should then be glued together with PVA glue. Leave for 24 hours.

You can then saw the finished shape and plane/sand the faces to a fine finish using increasingly fine grades of paper finishing with 400 grit. Finish with either wax or oil.