Place the Casting Basin under the Seared Faucet on the Smeltery Drain. When the metal has been liquefied, right-click the Faucet to pour the metal into the Casting Basin. After it cools, you will have a solid block of that metal.
The basin holds 9 ingots of metal, which equates to 4.5 blocks of raw ore. It's not currently possible to empty out a partially-filled basin, except by filling it fully or by dismantling it with a pickaxe and re-placing it. Consider using the Casting Table and an ingot mold to pour out excess ingots that aren't a multiple of 9 instead.
Placing a hopper under the Casting Basin will allow the automated removal of cooled blocks from the Casting Basin.
The casting basin is also used to make Brownstone blocks, by pouring molten tin over gravel. To do this, first right-click with gravel in hand to place it into the basin, then right-click the faucet.