The Smeltery is a multiblock structure (that is, it requires multiple blocks in a specific pattern to function, like a Nether Portal) that is used to melt metals at the cost of Lava. 

 

To construct the Smeltery, make a structure where all the walls and the floor are made of Seared Stone, Bricks, Windows, or pretty much any other Seared block. One of the blocks has to be a Smeltery Controller, which is where you can insert items. The Seared Tank holds Lava to fuel the Smeltery.

To insert/extract fluids, the Smeltery needs a Seared Drain with a Seared Faucet (Fluidducts work as well) attached to it.  The Faucet will pour fluids from the block it's placed on into the block it's directly above. It can be activated by right clicking or giving it a redstone signal. Under the Faucet, place a Casting Table (or a Casting Basin, if you want to make blocks instead of items).

You can make the Smeltery in any size as long as it is rectangular.
The more blocks on the inside of the Smeltery, the more slots there are available to use. 

Open up the Smeltery Controller and you can insert metals. If it has Lava, it will start to heat up, and then turn into molten metal. One ingot is usually equal to 144mB of that metal.

 

By default, melting ores will give you two ingots' worth of molten metal, effectively doubling your ores. Some modpacks may have this disabled.

Certain combinations of molten metals will create alloys. If two molten metals that are in a Smeltery can alloy together, they will, so be careful what metals you put into a Smeltery at the same time.

One part Gold and one part Silver will alloy into two parts Electrum.

Newly molten metals will go to the top of the stack, and things at the bottom are cast first. You can click a molten metal to send it to the bottom so you can cast it. 

To make a Cast, make a tool part out of a cheap material you don't mind losing and place it in the Casting Table. Melt 2 ingots of Gold or 1 ingot of Aluminium Brass and then right click the Faucet to pour the molten metal onto the tool part. This will create a reusable Cast for metal parts, destroying the tool part you used in the process.  

You can do the same thing with 2 Clay balls to make a Clay Cast, which breaks after one use but is much cheaper. 

To make a metal tool part, place a Cast into the Casting Table and activate the Faucet, and the molten metal will pour into the Cast and harden. Right click the Casting Table again to take out the metal tool part.