There is no singular purpose driving the Red Guild. It is a rather informal association without any strict hierarchy. Some would perhaps say that the purpose of the Red Guild is to simply make money in whatever way - scrupulous or not - they desire.
The random guildhalls scattered throughout the world all cater to different areas of interest. Some are simply unscrupulous merchants and moneylenders, some peddle occult artifacts and traffic in
dark magic. Another might be an alliance of brothel keepers within a city. The vast majority are composed of the standard criminal faire - smugglers, fencers, bandits, mercenaries, and so on.
No two guildhalls are ever exactly alike.
There is no unifying structure of the Red Guild and it often varies according to the guildhall one happens to be visiting. It is not a very centralized organization. The head (or heads, in some cases) of a guildhall are generally referred to as Guildmaster, while those under them might go by any number of titles, or none at all.
Still, there is some method to the guild's general madness.
The signature dye of the Red Guild is a still a closely kept secret, and they are known to still produce it and color garments with it. But they can still only be found among its closely associated members. Some might only be given a guild-red patch of cloth to sew into their garments, others might be given cowls or armbands.
Those rare few who know the means of making guild-red dye are simply called Dyers, and they are usually the ones who establish new branches of the guild. Dyers are a secretive bunch, often keeping their identity a secret. Not every Guildmaster is a Dyer, and some Dyers are Guildmasters.
Members of the guild are obligated to follow a sometimes written "Red Code." The most generally accepted precepts of the Red Code are to stay out of one another's business unless invited, offer assistance in times of need if asked, and offer favorable deals to guildmates when able. How seriously this code is taken depends on the guildhall or the member in question, but it usually keeps them from murdering one another outright.
Usually.