If you visit the NPC in Bichon (Near Weapon Vendor) they have two options for accessory refining, the first is where you add the accessory you want to level up in the top box and then matching accessories (by type, they don’t need the same stats) in the lower boxes. Once an accessory reaches 100% it will level up and the second refine option can be used, here you place the accessory you want to upgrade in the box and select the stat you would like it to be upgraded with from the options.
Accessories can be levelled up 5 (or maybe 6) times in total, the amount of matching accessories increases with each level ( Lv.1>Lv.2 takes 5 on a standard item, then Lv.2>Lv.3 takes 20 and so on - Lv.1>Lv.2 on a superior item only takes 1 for the first, then Lv.2>Lv.3 takes 4 etc etc).
It’s worth noting that you can’t break an accessory from refining and it has 100% success rate, one thing to remember is that refined stats can’t be removed (for now anyway) so make sure you are putting the right stats on your items... you’d be surprised at some of the horrifically refined items out there that started with decent stats.
Finally, most people look to refine accessories that have already dropped with added stats rather than just basic items, obviously this will depend on your end goal with the item and the stats you want to achieve.
Good luck and enjoy refining ^___^
XIII