Smelting in TFC is the process of refining ore into metal. It is a lot more complicated than in Minecraft, and this article will briefly cover the main points of smelting.
In the early game, players are restricted to smelting copper and copper alloys, such as bronze, using pit kilns. Metal ore is placed within a ceramic pot, and then heated in the pit kiln until it liquifies. Right-clicking while holding the pot will present an interface in which to retrieve the metal, using ceramic molds. While the metal is still liquid, it can then be poured from the ceramic mold into a tool mold, or it can be left in the mold to produce ingots.
The bloomery is used to produce wrought iron, an intermediary step towards producing steel. Wrought iron functions roughly as regular iron in vanilla Minecraft. The bloomery is used only for wrought iron. After firing coal and iron ore in the bloomery, a bloom is produced, which must then be worked at an anvil to produce a refined iron bloom, which must then be melted at a forge. If there's an empty ceramic mold in the side slot, the melted wrought iron will pour into the mold (without a mold, the iron will be lost as it melts).
Placing a crucible over a lit forge allows for smelting metals directly at the forge, allowing you to make more advanced alloys. This is where you can make the final tier steels of the game - Red steel and Blue steel. These alloys not only provide the best quality tools and armour, but they can also be used to smith red and blue steel buckets. These buckets are the only buckets capable of moving water/lava source blocks.