You take wood chips (typically from lumber rejects or sawdust) and mix it with caustic, a few other chemicals, and steam to break down the lignin (connective gunk between pulp fibers). You then wash the pulp to get the broken down lignin out (sticky, smelly, and really dark). The lignin stream is burned to recover the caustic and generate the steam. The pulp gets mixed with additives and more water and sprayed onto a really fast moving wire mesh. The wire carries the pulp through presses and then dryers to remove 95-97% of the water. The pulp is now paper that can be wound onto a reel.
The reel is cut into smaller rolls and put on a corrugator. The corrugator takes one of the rolls and flutes it. The box machine takes two rolls of flat paper and one roll of fluting and glues them together. It then prints the box info and cuts out the box. Another machine folds the box and glues the final seam.