There are 3 things you can refine:
1.) Equipment
2.) Sylph equipment
3.) Eudaemon Equipment
Equipment
You use normal refinement crystals to refine orange or lower quality equipments. When you upgrade it to mythic, the refinement levels wont reset, but afterwards, you can use only elite refinement crystals. With the new system, it is a good idea to refine your orange item to 5 level 10 stats before you upgrade it to mythic:
Because after you make it mythic, you just use need to use a few sets of elite refinement crystals for best effect. Sadly, for this you needed to save up refinement crystals, AND not upgrade your item to mythic yet. Don't forget, elite crystals are still worth to use, because red refinement gives better stats for the same level.
Sylph equipment
This is especially actual, since the golden holy water sipper hot event is running now. You get bonus to golden holy water used! Some weeks later I discovered I lost many items from my mail. If it was my mistake or a bug, I can't be sure, but I wasn't compensated. Among other stuff, I lost 9999 golden holy water. (Morale of the story: don't keep ANYTHING important in mail-inventory). Fortunately, I still had some 3000 left, so I could refine all my sylph equipment still, like this:
The sad thing is, now everyone can do this, don't need strategy in refining, you just keep clicking, and you get it maxed in no time. For max. effect you might want to use some bound balens for locking, but even that is not really necessary.
Eudaemon equipment
Eudaemon equipment is special in 2 ways: first, refinement materials cost balens (and a lot!) you can't get them for free. And you need a different one for every color quality. For pre-purple, I suggest only use the few free refinement itemy you got from chests eariler. For refining purple, you might want to spend some balens. It is still very expensive, and eudaemon is not that important; but now it's defintely more efficient to do this than before.