Refining can be done using the blacksmith in reboldeaux. The system is simplistic, 4 of a mineral are needed to make a refined mineral and 3 of a refined mineral to make a pure mineral. Pure versions are worth more vis than unrefined versions however it is ill-advised, since the quantity of minerals used to make these refined and pure minerals actually means you end up losing money.

The data below is from the Blacksmith in Reboldeaux. Refinement of cloth can be performed in Coimbra, but there is no data as of yet for it. Data taken with permission from noodles on the SOTNW forums.

I've calculated that (apart from with talt) refining minerals lowers their value.

Not having a high-eoughhigh-enough level to enter harder dungeons, my findings only go up to quartz, but it shows that the more expensive the base mineral, the greater the loss upon refining. I also have metal refining stats.

refinement guide (* indicates best value for money):

u = unrefined, r = refined, p = pure

talt:
u: 18
r(x4): 90 (profit of 18 ea)
p(x12): 300 * (profit of 84 ea)

ionium:
u: 31 *
r(x4): 120 (loss of 4 ea)
p(x12): 350 (loss of 22 ea)

quartz:
u: 43 *
r(x4): 165 (loss of 7 ea)
p(x12): 400 (loss of 116 ea)

aidanium:
u: 56
r(x4): 180 (loss of 64 ea)
p(x12): 450 (loss of 222 ea)

etretanium:
u: 75 *
r(x4): 195 (loss of 105 ea)
p(x12): 500 (loss of 400 ea)

metals:

copper piece: 12 *
bulk coal: 37 *
iron piece: 25 *

steel piece(1x iron, 1x bulk coal): 50
profit made from making: -12

cast iron for man(4x iron, 4x bulk coal, 1x copper piece):
profit made from making; -10

steel for man(5x iron, 6x bulk coal): 300
profit made from making: -47

Item worth (from best value for money refinement):

talt (pure): 25
ionium (unrefined): 31
quartz (unrefined): 43
aidanium (unrefined): 56
etretanium (unrefined): 75
copper piece (unrefined): 12
bulk coal (unrefined): 37
iron piece (unrefined): 25