Don’t forget that there are two different “making things” menus.
Crafting uses “&” (Shift+7 on most keyboards). I believe there was a charcoal kiln craft option in this menu, but I’ve always preferred the one you make using construction because I usually end up with a static base for a long time. I’ve never used the “crafted” kiln so I can’t tell you how it works.
Construction uses “*” (Shift+ 8 on most keyboards, or you could use the one on the Number pad. its right above the “9” there, no Shift necessary). That is the one I am more familiar with.
Once the kiln is made you’ll need to fill it, the more you fill it the more charcoal you’ll get (I believe that a full kiln will yield 250 charcoal). Once it’s full you will need to fire the kiln. The last time I tried it, the game required a nearby fire source to do so, which means that unless that has changed it’s probably a good idea to build a wood burning stove/fireplace, deploy a brazier near the kiln, or construct the kiln near one of the aforementioned. After firing and closing the kiln (accomplished by examining it) you will need to wait some time to get your charcoal.