How do I make a cardboard box stiff or solid enough to put things on?

Get a moving box the right size, cover with a table cloth and you have a table. If you are using the side of it, be sure to tape it securely closed. I used one for an end table for quite a while when my kids were small. I had a glass lamp, that I put on that table and it was fine with that and with the other decor that I added. You cannot sit on it! Unless of course you have it solidly filled and taped.

Build a grid like the ones used in wine packing boxes to fit you box. I have been making small foot rest out of boot boxes by using this method they have held up quire well. My grandchildren have even used them to sit on.

Double it up. But if you cannot stuff the box with old clothing or rags you no longer need tape box up well and wrap it with a beautiful fabric. Sit a mirrored tray on it or a mall slab wood for a nice table top.

why?? just buy or build furniture - watch the side of the road - toss the cardboard.