Short answers, pulled from the story.
Puddling is the process of converting pig iron to wrought iron in a coal-fired reverberatory furnace. Workers stirred molten pig iron with long hooked bars called rabbles in an oxidising atmosphere, burning off the carbon until the iron reached a pasty consistency and could be gathered into a ball and rolled.
Henry Cort at Fontley in Hampshire refined and patented the puddling process in 1784. Peter Onions at Dowlais had earlier begun successful commercial puddling in 1783, and the Cranage brothers received patent number 851 in 1766 for an experimental version that was never used commercially.
Dry puddling first refined pig iron into 'finers metal' in a separate hearth before charging the puddling furnace, and yielded about 77% of the input as iron. Wet puddling, invented by Joseph Hall at Tipton, added iron oxides to the charge, causing violent boiling and achieving a yield of nearly 100%.
Puddlers typically died in their thirties due to the strenuous labour, extreme heat, and fumes from working the furnaces. A puddler and helper could produce roughly 1500 kg of iron in a twelve-hour shift, stirring hundreds of pounds of molten metal by hand through the entire process.
Puddling was displaced by the Bessemer process, which could handle charges of 15 short tons compared to the 800-900 pound limit of a puddling furnace. The process could never be automated or scaled, because the puddler had to judge by physical sense when the iron had reached the right consistency.
The Eiffel Tower, the original framework of the Statue of Liberty, and 19th century iron bridges were all built from puddled iron. Puddled steel also remained the main raw material for Krupp cast steel as late as the 1870s.