Building a humidor can be a challenging project. If you are competent or skilled working with wood, Fine Woodworking has a great video on the web that shows you how to build your own humidor.
For the rest of us mortals, we will have to make do with purchasing a humidor. It is easy, convenient and cheap. Yes, you heard right. Cheap. We have a great selection of fine humidors at very low prices.
But there are other options. You can build a cheap cigar humidor using a cooler or a Tupperware container. If you find a fine cigar box that closes tight you can buy a humidor kit (hygrometer and humidifier) and stick it to your box with non-odorous glue or double face tape.
You can also build a large cigar humidor out of an old refrigerator or other large piece of furniture, but this is tricky, so be careful and make sure the furniture can take the stress of retaining moisture in the long term. Planked panels may warp, some finishes on furniture may be slighly toxic or the wood used (especially plywood) can give off noxious gases. Particle board panels, which are quite commen, will swell and crumple into dust after being exposed to moisture for a long time. So any furniture that you convert you must consider lining with Spanish cedar and adding additional bracing and/or support.
Tip: If you're looking for a humidification system, here is a nice info-graphic to help you choose the Humidifier what will work best for your needs: