In the case of the Mongols and Jurchens/Manchus, there were three major sources: trade, self-manufacture, and (most interestingly) the forest peoples living north of the steppe belt.

We know that the Mongols and Manchus desired to trade for iron, because the Ming Dynasty in China (1368-1644) and Joseon Korea (1392-1910) banned the sale of iron, weapons, tools, and armor to steppe nomads out of fear that the trade would arm their historical enemies. The same phenomena - and reasoning - are also largely true for the trade between Muscovy/Russia and the Crimeans and Kalmyks in the 15th and 16th centuries. The era I'm talking about here was after the fall of the Mongol empire, but the model of trade - and restriction of trade - extended back to the eleventh and twelfth centuries when the Mongols traded with first the Khitan Liao Dynasty (907-1127) and the Jurchen Jin Dynasty (1115-1234).

In the case of the Manchus, they simply conquered regions that produced or traded in iron. The Manchu ruler Nurhaci originally purchased iron from the Ming and Joseon Korea, but after the sale of iron to nomads was once again banned, his capture of Kaiyuan and Tieling gave him access to the iron mines, laborers, and trade routes he needed to produce weapons.

Metalworking skills were not unknown among the Mongols, but it was less common given their nomadic way of life. That's why, during the period of Mongol ascendancy, they turned towards the forested regions north of the steppe, where the people living on the Amur and Yenesei rivers were more or less sedentary (to my knowledge). The Amur and Yenesei populations possessed sophisticated metalworking techniques, and the difficulty of procuring iron and weapons from southern sedentary empires like China and Byzantium mean these forest zones were a more readily accessible source of skills for the Mongols. Co-opting these peoples was actually more difficult in some cases, because they did not possess pre-existing, large-scale administrative structures that the Mongols could subsume and adapt for their own purposes after conquest. Thus, the Mongols tended to leave the Amur and Yenesei river populations alone and ruled through existing familial networks, in exchange for the services of skilled ironworkers.

Sources: Thomas Allsen, "Technologies of Governance in the Mongol Empire: a Geographic Overview," in David Sneath, ed. Imperial Statecraft: Political Forms and Techniques of Governance in Inner Asia, Sixth-Twentieth Centuries
Evelyn Rawski, Early-Modern China and Northeast Asia: Cross-Border Perspectives
David Khodarkovsky, Russia's Steppe Frontier: The Making of a Colonial Empire, 1500-1800, and Khodarkovsky, Where Two Worlds Met: The Russian State and the Kalmyk Nomads 1600-1771
Henry Serruys, "Sino-Mongol Relations During the Ming, III: Trade Relations: the Horse Fairs (1400-1600)," in Mélanges chinois et bouddhiques vol. 17