What do charters for guilds consist of? If all the alchemist guild has is wildfire, how to they sustain themselves? What does the Royal charter for the faith or citadel consist of?

Well, much like city charters, guild charters gave guilds legal recognition, rights, privileges, responsibilities, and limits. 

So what kinds of “rights, privileges, responsibilities, and limits” did these charters include? 

• First, guild charters gave guilds a legal monopoly over a given trade or industry. If you wanted to work in a given industry in a given location, you had to be a member in good standing who had been given permission to work in that town or city. On the other side, employers and merchants who wanted to hire a smith or buy their goods also had to do so with a guild member, lest they be legally liable. 
• Next, guild charters gave guilds control of training, licensing, and locating of workers in their field. In order to become a member of the guild, you had to go through a guild apprenticeship where you would live with a master craftsman and labor for them for anywhere between seven and fourteen years. Apprentices were not paid save for food and lodging, but their masters were required to train them in the skills and trade secrets of their industry. When you had completed your education, you would be licensed as a journeyman, be given a set of tools that were now your property,  and could now work for wages in your field. Journeymen were usually sent away from their home city for a period of at least three years (although that’s not where the name came from), for reasons that I’ll explain later. When you had completed that process and could afford to pay the application fee, you could apply to become a master craftsman, by submitting a masterpiece (that’s where the name comes from) to the guild masters for their approval – if your work was up to snuff and the guild masters let you in, you’d now be a full member of your field with the right to open your own business, hire journeymen, and train apprentices (indeed, you were required to train apprentices). 
• Third, guild charters gave guilds wide powers of regulation and self-regulation. In addition to the right to charge membership dues, guilds also had the right to fine members or even expel them for violating the regulations of the guild, and guilds established extensive regulations on prices, wages, working conditions, product quality, even standards of personal behavior. (Guild members could be fined or even expelled for drunkenness, for example, because it threatened the guild’s reputation for quality labor). At the same time, guilds also used their control over their members to essentially bargain collectively with governments, suppliers, merchants and employers, wielding the authority to blackball them from doing any business with guild members to get their way. 

So how did the guilds use these powers? 

First, they used them to control labor supply, labor demand, prices and wages – guilds carefully manipulated the intake of apprentices, the licensing of journeymen, and the qualification of masters, and used their powers to permit working or operating a shop in a given town/city/region, to ensure that there would be enough work/consumer demand for their members at the wages/prices necessary to support the living standards of guild members. If there wasn’t enough work to go around in a given location, journeymen would be refused entry to a given town and sent on their way, and masters would be refused the right to open a shop. 

Second, they used them to control the quality of goods and services – if you sold shoddy goods or did shoddy work, the guild would fine or expel you, and if you tried to work in their industry without going through their training process, you’d be prosecuted. 

And third, they used them to create mini-welfare states – financed by the various dues and fees they charged their members, guilds operated pensions for the elderly, the disabled, widows and orphans, a system of unemployment benefits for journeymen who couldn’t find work, and funeral benefits. 

As for Westeros, the guilds we know about are the Alchemist Guild in King’s Landing, the Guild of Smiths in King’s Landing, and a series of unnamed guilds in Oldtown. The Faith isn’t a chartered institution – it’s a religious institution – but the Citadel might have a charter from King Urrigon Hightower, but we don’t have direct confirmation.