Craft a Mortar and Pestle or use an Industrial Cooker
Gather water in a Waterskin, Water Jar, or Canteen
Place the correct ingredients for the dye color into the crafting station
Add charcoal, sparkpowder, or gunpowder as the fuel ingredient
Make sure the container has water in it if using a Mortar and Pestle
Start crafting to produce the dye
Use the dye on armor, weapons, structures, or other paintable items
Collect dye from the Industrial Cooker if crafting there
Repeat with different ingredient combinations for different colors