I have heard that leaving a large pile of burnt wood ash out for a long time turns it into caustic lye. I am having trouble understanding this, as lye is a very strong base and would react with the air and water around it. How is this process done in nature? I don’t want to burn my hand off when I don’t have the fire pit lit!
Can’t speak to the chemistry of the situation, but I’ve made the mistake of leaving charcoal ashes in the backyard grill after a rainfall. The water trickling through the ash becomes decidedly caustic. It will eat the bottom out of the grill basin eventually.
Of course, ordinary water could do that to an iron/steel basin, but I always put the coals on a layer of aluminum foil to make it easier to remove the ashes later. After a couple of days of neglect, I’ll find a nice round hole eaten through the foil, wherever the damp ashes were touching it.
The word lye is imprecise, since it can refer to any strong alkali (nowadays it most often refers to potassium hydroxide or sodium hydroxide). The stuff you buy at the store that’s labelled “Lye” is usually sodium hydroxide. The stuff you get from wood ashes, although sometimes called lye (especially in the past), is actually potassium carbonate (also called “potash”, another imprecise term), which is not nearly as strong a base as the hydroxides.
Traditional soapmaking calls for leaching wood ashes with water. The water will dissolve the potassium carbonate and later react with the fatty acids to make soap.
If I understand the process properly, potassium hydroxide (wood ash lye, KOH) is a by-product of the combustion process that happens to be water-soluble. The ash doesn’t change, the water just leaches the hydroxide out of it. KOH ionizes completely in solution, producing an extremely caustic liquid. Evaporation will precipitate white crystals of KOH. AFAIK, it does not react significantly with air either in solution or in crystalline form. As bibliophage pointed out, the solution will also contain potassium carbonate. I’m not sure what the proportions of the two are–I think it will vary with the type of ash.
Essentially, you rinse really harsh soap out of the ashes. Wear gloves when cleaning the firepit–it’s unlikely to burn you (unless it’s been building up for a long while), but it’s not at all good for your skin.
If you don’t want to burn your hands off let the fire die and the coals go out.
Outside of that just wash your hands.
The lye is concentrated in the water used to wash the solution out of the ashes.
From what I have read the old timers used a stick if they needed to do something in the hopper where the lye water was working.
The lye water was poured through the ashes several times until it reached the correct strength.
Just a note on the semantics of the original question:
You can not leach lye from charcoal. You can leach lye from wood ashes.
Charcoal is almost pure Carbon.
Er. I think it’s not soap; it’s just lye. For soap, you have to combine the lye with fat.
Yes, for true soap you have to use the lye water to saponify fats (I just knew someone would call me on that). However, lye water alone can be used as a harsh cleansing agent (I don’t recommend it) and has a slick, soapy feel to it. It won’t lather, though, as far as I know.
Nope, it won’t lather. 
In fact, depending on what your proportion of fats to lye is, sometimes the soap itself won’t lather until it’s had a chance to sit for a few days (i.e., for saponification to occur more thoroughly). It depends on the formula you use.
(I make soap at home, which is why I know this stuff.)