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There's two ways:

Events. At an event, you may find equipment made from the desired material. If you really want, you can spend Goodwill to get an event specifically to find equipment or refined and usable materials as well.

Institutions. This is much more involved, but much more consistent.

There's a three step process to access any material:
- You have to extract it, such as through a mine.
- You have to refine it, such as through a smelter.
- You have to work it, such as at a smithy.

The exact cost of doing so varies depending on the material in question, and will be outlined on each page's entry. It should be noted that refineries and artisans have no upper limit on the amount of goods they can process; if you want to build just a mine and rely on someone else's institutions to refine and work the material, that is cheaper. It is also riskier, as the creation of a supply line means that someone could ambush it, and business relationships can break down.

Once these institutions have been created and you have a ready means of accessing the material, you can just start making stuff out of it. If you are the only place in the world that makes a given material, then you control the global supply of it and anyone else who wants it either has to invest into their own institutions or go through you to access the material. There is no limit on how much you can make, except with regards to NPC armies. One mine can support one army, and will need to be fed with more mines in order to support larger armies.