Furnaces and Smelting
Furnaces are used for smelting ore to turn it into usable metal. They are also used to turn sand into glass, to bake clay into bricks and to turn cobblestone back into smooth stone.
Furnaces are also used for cooking food.
Making a Furnace
Furnaces are made by combining 8 cobblestone blocks on a crafting table.
Using a furnace
When you right-click on a furnace, you are presented with a new version of your inventory screen:
Place fuel in the lower slot and the items to be cooked or smelted in the upper slot. When done, the product will appear to the right.
Fuel for your furnace
Coal
You will mostly use coal for smelting and cooking. It's very abundant and once you start mining and exploring underground you'll have more than you know what to do with. However, there are other options if you need them. One piece of coal burns long enough to smelt or cook 8 items.
Wood
Wood blocks, wooden planks, sticks and tree saplings can all be used as fuel.
If needed, you can also burn wooden tools, chests, bookshelves, stairs, fences and other wooden items.
The most efficient way to use wood as a fuel is to make charcoal.
Charcoal
Charcoal is a form of coal that is made by baking wood blocks in a furnace. It has exactly the same properties as coal; it is an efficient fuel and can be used to make torches.
To make charcoal efficently, bake one or more wood blocks into charcoal, then use that charcoal as a fuel to bake more wood blocks.
Other Fuels
Lava buckets and blaze rods will also act as fuel. Lava buckets provide enough heat to cook 100 items (and yes, you do get the empty bucket back afterwards).