The box goes together as two separate pieces, lid and base, so mark all the components as to where they are going to fit, base or lid, left or right, front or back and do a trial assembly. If you have clamps this is much easier.
For my first box, I used both wood glue and screws. First drilling screw holes in the edge, then applying the glue to an edge, and finally fixing them together with screws. This worked very well but a bit fiddly.
Having found that the glue was very strong in my case, the second box was glued and clamped which was much easier to do and appears to be just as strong.