Sulfide smelting generally involves roasting (heating in oxygen-rich environment) to convert metallic sulfides to smelting-friendly ores, and then subsequent smelting. It doesn't seem that Roman artisans often smelted their silver from sulfides, though--they mainly recovered silver from lead and copper ores. I can source two excerpts from "The Substance of Civilization" by Stephen L. Sass:

Unlike gold, metallic silver rarely occurs in nature, since it reacts rapidly with gases in water and air to form silver sulfide compounds (or tarnish). Gold and silver are frequently found together in an alloy called "electrum," a favorite of ancient artisans for use in decoration...

By far the largest sources of silver in the ancient world were lead ores, but until metallurgists discovered how to smelt them very little silver was available to artisans. To extract their precious prize, smelters first reduced the ore to lead containing small quantities of silver. Then, in a process called "cupellation," they oxidized the lead in a shallow porous cup (a "cupel"), by heating it to temperatures above the melting point of silver, 961 degrees. The lead oxide vaporized and was absorbed in porous bone or ground-up pottery shards in the cupel, leaving behind a shining globule of silver...

At the beginning of the Common Era, the richest mines were capable of yielding merely ten pounds of silver from a ton of lead.

Regarding silver extraction from copper:

Continually pressured by their imperial masters to increase the output of the Spanish mines, Roman smelters pioneered a variety of innovative techniques, including "amalgamation," or dissolution of precious metals from pulverized ores into liquid mercury. Subsequent distillation of the mercury left behind gold and silver. The Romans obtained mercury from their mines at Almaden in Spain by heating a reddish-orange mineral called cinnabar, mercury sulfide, and decomposing it into sulfur dioxide and liquid metal.

Seeking to further improve the extraction of minuscule amounts of gold and silver from their Iberian mines, Roman smelters then devised the process called "liquation." Taking advantage of the greater solubility of gold and silver in lead than copper, smelters melted copper containing these metals, together with large quantities of lead, which absorbed them. Since copper and lead are not soluble in each other, and lead melts at a much lower temperature (328 degrees) than copper (1083 degrees), the lead and copper could be separated by gentle heating, allowing the liquid lead, laden with gold and silver, to drain off. Cupellation then recovered the precious metals from the lead.

If it wasn't clear, the degrees referred to in these excerpts are in Celsius.

Regarding the extraction of silver from the gold-silver alloy (electrum), some gold parting techniques existed (using salt to react and precipitate the resulting silver chloride out in water). Gold parting was important since electrum coins would have huge variations in value depending on their supposed gold content.

In terms of characterizing ancient coins for the sources of Roman-era silver, cupellation as a refining technique exhibits itself in trace quantities of lead, bismuth, and gold in the produced silver bullions as these elements are relatively unaffected by the process. So we have some indication of the possible ore type from which the silver was extracted based on the exact composition of the impure silver.

You can also check out "The Metallurgy of Roman Silver Coinage" by Butcher and Ponting for more specific material (pages 100-103 detail the possible and likely sources of silver).