Unlike a gas grill where you can dial a temperature and turn the fuel off and on, charcoal is a volatile material and will burn until it ashes out.
The easiest way to put out a charcoal grill is by closing the exhaust vents. By closing the exhaust vent, you prevent the draft from occurring that causes air to pull through the intake damper. You also prevent combustion gases and smoke from escaping - which smothers the fire.
The easiest way to understand how a charcoal-fueled grill works is by looking at the "Fire Triangle."
The Fire Triangle or Combustion Triangle tells us that three elements need to be present in order to ignite a fire: heat, fuel, and oxygen.
In our case, the fuel is the charcoal, oxygen is around us at all times, and the heat comes in the form of lit briquettes or lump charcoal via a charcoal chimney - usually started with a firelighter of some sort.
When any of these three elements is removed, a fire can't be present.
This model is useful to understand because it tells us how to go about putting out a charcoal grill - oxygen.
There are a couple of ways to put out a charcoal grill, however, the easiest is by closing the exhaust damper.
The exhaust damper - also called a vent, flue, or chimney - is found on the lid of a charcoal grill.
The exhaust damper should be partially open at all times as it creates a pressurized draft that pulls oxygen through the system; It also allows for combustion gases to escape.
Since our goal is to stop or put out the charcoal, by closing the exhaust damper we effectively prevent these things from occurring.
The inevitable result is that no oxygen is pulled through the system and the combustion gases (Carbon Monoxide, Carbon Dioxide, and others) from the charcoal will smother the fire and displace the oxygen.
From the Combustion Triangle above, if we have no oxygen, we have no fire.
When learning how to control a charcoal grill's temperature, I always advise that folks adjust the intake as apposed to the exhaust.
The exhaust damper is usually more than enough to put out a charcoal grill. However, you could also starve the fire of oxygen by closing the intake damper which would cause the fire to burn out.
Even with the exhaust damper open, if you were to close the intake damper, the fire would eventually die out as there is no oxygen entering the system.
In order to do this, you simply close the intake damper (pictured below).
On most charcoal grills, the intake is how you control temperature.
To put it simply: When the intake damper is open all the way, more oxygen enters the system and the temperature rises; As you close the intake damper, less oxygen enters the system and the temperature drops.
Meaning, if the intake is entirely closed, the temperature drops off markedly until the fire burns out.
This is highly dependent on the amount of lit charcoal you added to the grill. As you can assume, the more lit charcoal, the hotter the fire.
If you're smoking meat, you may only add a few lit coals that then progressively self-ignite.
Grills like the Weber Kettle are also made of steel that's coated in porcelain enamel. Meaning, they're insulated quite well and simply closing the vents won't instantaneously drop the temperature.
The charcoal that's within the chamber will still hold it's temperature quite well and it will take roughly 4-8 hours for the grill to cool down. In some cases it can take up to 48 hours for the embers to completely die down.
Just as an example, I've recently been testing lump charcoal and loaded up a base layer of Royal Oak and then poured a lit chimney of Royal Oak lump charcoal on top.
The resulting fire was 600F as measured by the lid thermometer. I then made my version of smash burgers on the Weber kettle (essentially without a fat or a skillet).
When I was done grilling my burgers, I closed the exhaust and closed the intake. The temperature went from 600F to well below the 150F mark in roughly 45 minutes. The temperature outside was roughly 60F.
The lid was warm to the touch and sat in my driveway for another 3 hours until entirely cold to the touch.
While waiting for your charcoal to cool, keep the lid on and keep the grill out of the way. I'd also refrain from using the grill cover, unless the temperature gauge on the lid is near 0F.
I've seen several websites tell people to spray the hot coals with either a hose or a spray bottle of some sort to douse the fire.
This method is in a similar vein to pouring water on a camp-fire; The charcoal brand Kingsford even recommends this.
However, I'd personally never and I mean ever do this to my charcoal grill.
For starters, you have the chance of thermal shock which could crack and ruin your grill. On Weber's website they even note that issues like Thermal Shock aren't backed by their warranty.
To quote them:
"Do not use water to control flames or put out charcoal"Weber
Secondly, the mess that this could make is enough to deter me. While I'm by no means afraid of a little dirt, I'm not too keen on ruining my dampers due to the potential sludge build-up. Needless to say, this makes an already hard job, more difficult.
Thirdly, pouring water on top of lit coals creates steam, which is a potential burn hazard.
Any coals that haven't entirely ashed over and don't crumble away are safe to use. I'll typically take the remains of my grilling sessions and dump them into my charcoal chimney to use in the next cook.
With briquettes, this is readily apparent as the briquette will no longer have shape and fall away when you try to pick them up with tongs.
Any briquettes that still hold their shape and aren't entirely ashed over (are black and grey) are perfectly fine to use.
Lump charcoal will also readily ash - it produces far less ash than briquettes - any useful pieces will be readily apparent.
I always recommend using an old pair of tongs to move charcoal - unless you know it's cooled down and safe to move.