The kiln is a multi-block structure built out of bricks over stoked hibachis, used to fire pottery, burn wood into charcoal, separate end stone into brimstone and white cobble, and perform some of the functionality of the brick oven without requiring fuel.

The structure consists of an open block for the item to be fired, with brick blocks enclosing it on the bottom and at least 3 other sides. One block beneath the brick base must be a lit hibachi stoked by bellows. Having more than one hibachi speeds up the progress, like the cauldron, with a max of 9 hibachis in a 3x3 square. The kiln is necessary to obtain a crucible.

Applications

Making Pottery (Crucibles, Planters, Vases, Urns and Moulds)
Smelting Ores
Burning Wood into Charcoal
Baking Clay into Bricks and Nether Sludge into Nether Bricks
Baking Bread Dough into Bread, Cookie Dough into Cookies, Oven Ready Pumpkin Pie into Pumpkin Pie, and Cake Batter into Cake.
Separating End Stone into Ender Slag and White Cobble

Cooking time

The kiln must tick 15 times to cook its block. The tick rate is calculated with this formula:

T = 120 * ((8 - (#fires - 1)) / 8) + 40.

Additional multipliers are applied to the above base times based on the recipe:

Food: 1x
Pottery: 4x
Ores, End Stone, and Logs: 8x

Therefore, the cook times for the kiln are as follows:

Number of stoked fire	Cooking time (in game ticks) (1 second = 20 ticks)	Base cooking time for Food (in seconds)	Cooking time for Pottery (in seconds)	Cooking time for Ores, End Stone, and Logs (in seconds)
1	2400 ticks	120 seconds	480 seconds	960 seconds
2	2175 ticks	108.75 seconds	435 seconds	870 seconds
3	1950 ticks	97.5 seconds	390 seconds	780 seconds
4	1725 ticks	86.25 seconds	345 seconds	690 seconds
5	1500 ticks	75 seconds	300 seconds	600 seconds
6	1275 ticks	63.75 seconds	255 seconds	510 seconds
7	1050 ticks	52.5 seconds	210 seconds	420 seconds
8	825 ticks	41.25 seconds	165 seconds	330 seconds
9	600 ticks	30 seconds	120 seconds	240 seconds

Keep in mind

Three different valid configurations of the kiln being used to fire planters.

The kiln can be arranged in any fashion as long as the item to be fired is adjacent to 4 brick blocks, and one of those brick blocks is below it.
The bottom of the kiln must be two blocks above the hibachi, occupying the top block of the stoked fire.
Bricks can be made by applying a mortar (clay, nether sludge or Slimeballs) to loose bricks.
Any blocks can be placed above the fire (occupying the same space as the two-high fire block), this doesn't prevent the kiln from cooking, and allows the player to build a proper floor around the kiln, to make the area safer to navigate.

Early automation

An easy, early way to automate to cooking of ore blocks (made by crafting 9 ores into a block) is to use a kiln in a special shape, like pictured below.

Since ore blocks have gravity (like sand), ore blocks will cook one after the other, falling once the bottom one is cooked.
The cooked ingot will be pushed into the crucible for storage. To make sure the last ore block in the tower also gets pushed into the crucible, you need to top it off with 2 other gravity blocks, like loose cobble or sand.
Ideally, you want to have some blocks to the sides of the crucible (next to the bricks) to prevent the items from flying to the side and into the fire!

Tube kiln

A tube kiln is the community-made term for a series of contiguous kilns built in a tube shape.

Concept

Given the large amount of Planters and Soul Urns that are needed for making any kind of crop farm that doesn't require you to remove weeds in the morning, to craft Pistons to automate your farms and for Villager trading, you will want to seek ways to improve your kiln cooking capacity.

The most common way to achieve that is by building more kilns, and the most convenient shape for this is the tube kiln:

This is the most commonly used tube kiln, a series of 7 contiguous cross-shaped kilns
It requires 3 Bellows and 27 Hibachis
This gives the maximum cooking time to every Kiln, while using the least amount of Hibachis and Bellows
There is no kiln at both ends, even though there is a Hibachi under that could be used, because each kiln requires a 3x3 of stoked fire to cook at max speed

Here is a gallery showing a tube kiln

Using water and pistons

A tube kiln with water and pistons

To make it more convenient to place items in the kiln, you can add Sticky Pistons to move some brick blocks.

While you can technically refill it without using any piston, even just using one in the middle makes the process a lot easier.
The pistons can be placed on any side, depending on the shape you want your kiln to be once you decorate around it.
To make it even more convenient, using water, as well as a Crucible or a Cauldron at the end opposite to the water, will allow you to automate the process of collecting the items once they are cooked.
This is a great way to make sure you never lose a cooked item because you forgot to pick it up in time.
This is why tube kilns are not built more than 7 blocks long, because water only flows 8 blocks, and you need one extra block for the water to fall into the tube.

Fully-automated tube kiln

Let's go over the process of automating a tube kiln step-by-step. There is also a video at the end if you just want to copy the design, but this next section will help you understand how it works, so you can create your own contraption in the future!

Thanks to Hiracho for his amazingly simple design!

Fully-automated tube kiln guide
	The ideal way to handle cooking a large number of blocks is to use redstone to automate the entire process. This requires trading with a Librarian to be able to buy from him: 2 Block Dispenser 1 Detector Block 1 Buddy Block We'll also need to craft 4 Repeaters, which require Gold for the Clock. And finally, we use a Crucible at the end, to collect the items automatically when they flow above it. If you're cooking food in your kiln, remember that a stoked Crucible will destroy any food in its inventory (it burns them after a short delay). This is one of the reasons why we remove the Hibachi that is under the Crucible, but it's not the main reason (we'll see why further down)
	The first thing that we want to consider is the redstone part that will produce 7 "pulses", which will allow us to place 7 blocks with a Block Dispenser, and to push them into the tube kiln with a piston. By placing a Buddy Block above the place where the Block Dispenser will place blocks, and by making sure the Buddy Block is facing towards the Block Dispenser, we can cycle through the Block Dispenser's content. We place 6 different solid blocks inside the Block Dispenser, and a Redstone Torch in the last position. Every time the Block Dispenser picks up a block, the Buddy Block detects it and sends a new pulse, making the Block Dispenser place and pick up another block This goes on for every different solid block that is inside the Block Dispenser's inventory, which are placed in the order they are in, from left to right and top to bottom (see the next section below) Make sure you use different blocks for every slot, and that those blocks are considered solid, meaning that they can carry a redstone signal (unlike stairs, slabs, or glass blocks, as those won't work) If you decided to make a smaller tube kiln, just remove the necessary number of blocks from the Block Dispenser to give you fewer pulses
	The content of the Block Dispenser "pulser". We use a special property from the Buddy Block to prevent creating an infinite loop: It doesn't get triggered when a "redstone type" block gets removed. With 6 different blocks + 1 redstone torch, we get exactly 7 pulses, before the whole thing stops by itself. If you make your tube kiln shorter, just remove some solid blocks from the Block Dispenser.
	If we send those 7 pulses into another Block Dispenser paired with a Piston, we can push the blocks we want to cook inside the tube kiln.
	Just make sure that the Piston gets powered at least 2 ticks after the Block Dispenser. Otherwise, there isn't enough time for the Block Dispenser to place blocks before the piston gets extended.
	The next thing we need to consider is how we detect when our items are done cooking, and to trigger the pulse to push in the next batch. We use a Detector Block facing down to detect when the items start flowing towards the collection point. One EXTREMELY IMPORTANT detail here is that we remove one Hibachi, located just under the Crucible (in the picture I only unpowered the Hibachi, so you could notice its different texture). This is because we want the Block Detector to only trigger once, when everything is done cooking, and to give some time to the water and the items that are the furthest to flow towards the end. By making the "last" item cook slightly slower (it will be 20s more than the others), we're guaranteed to have every other item gathered close to the last one, ready to flow down towards the crucible at the same time. If you do not do this, the detector will send out multiple pulses when the items flow down one by one, messing up the process.
Words of caution
	Just to be sure you don't miss this part, I'll say it again: DO NOT PLACE A HIBACHI UNDER THE CRUCIBLE We want the last item to cook slightly slower, so that our Detector Block only sends a single pulse, otherwise items will float too slowly towards the end, and the whole timing gets messed up!
A picture is worth a thousand words, so a video is worth a thousand thousand words? Video showing the tube kiln in action, and the redstone, to help you rebuild this design
Load video Local File Local File might collect personal data.