There are a ton of crafting materials you will need to gather up to upgrade and make items in Biomutant. You can gather the mains ones, Duct tape, and planks by finding large totems in the game world and destroying them. However, if you are after weapon or armor parts, you will need to find and kill various enemies in the game or just buy them from vendors.
Along with this, certain quests can also be a good source of crafting materials if they reward them upon completion, and dismantling old items is always an option. You'll get a ton of loot and gear in the game, so we highly recommend dismantling the ones you don't want to sell or use to farm crafting materials.
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Doing so will allow you to get a steady flow of materials so that you can actually make stuff you want. However, you can also find many of the items you need by simply searching the environment and world. So we highly recommend exploring to see what you can find.
That being said, once you got a sizeable amount of materials, you will be able to craft and upgrade your weapons and armor by finding a workbench. You can find a workbench usually at both towns and outposts at the top of giant yellow balloons