Producing ingots with a bloomery takes 2 steps

Firstly, put the ore in the top, with some coal or charcoal, aswell as fuel. This will smelt into a bloom. (Iron ore smelts slower than other ores..)

With the bloom, right click the block with tongs, this will safely pick up the bloom(Do not pick it up from the GUI, you will burn yourself) If you drop the bloom, just walk into it with empty tongs. (you can't pick hot items up without tongs)

right click an anvil slot to place the bloom. and hammer it. This produces slag and a hot ingot, cool the ingot down by right clicking empty tongs, then right click water.

Bloomeries can be sped up when using bellows, You will need to keep pumping)

Slag can be placed on the ground, it's worthless really, just pile it somewhere, breaking it can recover flux and charcoal