Most of the parts of the box are held together with wood glue (wood glue is typically stronger than the wood itself). Above is a photo of the bottom being glued on.
Here, I have just applied the first coat of varnish to give a smooth, finished look. It brings out the warm tones in the wood (poplar). I used satin finish so it would not look too glossy, but have just a little shine. Next, a light sanding and a second coat.