This toy relies on glue to hold everything, so it's worth taking some time and reading the instructions on the glue bottle. I used Gorilla Glue, which recommends wetting the wood and clamping the pieces.
Some glues expand a lot during the drying process, so you'll learn how much to apply to fill the gap and get full adhesion, but avoiding too much spilling out in the cracks. If the glue does ooze out of the gaps, it's often better to let it dry and then cut the bubble with a sharp knife rather than wiping with a rag and smearing it all over the wood.
This is a jury-rigged setup I used to weigh and clamp the top hull layer: