Refinement is how you add the blue stats to your gear. Unlike enhancing though, refining is never 100%. Also unlike enhancing, costume items can't be refined until R6 (Recast 6) and R7 (Recast 7)

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If you want to refine your gear, just head over to a disassembler near one of the blacksmiths and choose the 3rd option. After the tab opens up you will need to put the piece of gear you want to refine on slot 1, followed by 3 items you want to sacrifice on slots 2, 3 and 4.

 

The easiest and quickest thing you can get to use as sacrifices for refining are the rare (blue) grade armor/weapons that the blacksmiths sell. They will give you a 60% success rate every time. You could always use other items as well to increase your chances but it's up to you. The success rate, materials and amount of gold you will need for the refinement will be displayed after you place all 4 items in each of their respective slots. An example is given below.