So, last year I took a blacksmithing class, and I learned a lot. Mostly I took it to learn what safety precautions were needed: wear eye protection, ear protection, natural-fiber clothing and closed footwear. Drink lots of water. Holler before you move around the shop carrying hot metal. Don't grab your tongs too close to the hot end. Since then, we've been slowly gathering tools and books to continue at home. One of my teenagers bought a small H. Freight anvil and was able to do a little work on it, offsite where he had access to a fire and could point a blow dryer at it.
Then two things happened: first, I found a larger and better small anvil at a yard sale for a reasonable price, and he found this video about a very basic dirt-insulated forge with a hair dryer blower. The forge burns charcoal, technically, but you can make the charcoal from firewood as you go, or use lump charcoal. Briquets don't burn hot enough, apparently.
Teenager, after some consultation, came up with a similar forge, using the lid from an old round barbecue grill for a dirt container and an old elementary school desk as a base, with a supporting structure in between.
The barbecue lid is of heavier metal than most, and even so needs the dirt sloped right up to the edge to protect the metal from overheating and burning out. It's also several inches deeper than most. The teenager didn't skimp on the dirt, and the firepot is shallower than the one in the video. It still works. When the blow dryer is running, the fire roars quietly. The supporting structure needs a little more heat protection around the top. The advantage over a wooden dirt box, which would have to be about as large as the one in the video, is portability. The advantage of blacksmithing at home is that you only have the heat of one little inferno to deal with.