While firearms do exist on Harth, they are essentially limited to the Isle of Vess, which is the only region where people have figured out how to produce gunpowder--and it's a closely-guarded secret. While it's not impossible for a player to get their hands on a firearm, it shouldn't be counted on--and securing a reliable source of gunpowder is even less likely. No characters start with proficiency in firearms (except with special permission), but Fighters and Artificers can figure out how to use them effectively with a week of practice. (Other characters may also be able to do so, on a case by case basis.)
The rules below are a tentative mix of the DMG's firearms rules and Matt Mercer's (neither of them are quite to my liking) and are subject to change.
A note: I do not apply disadvantage from being prone to attack rolls made with crossbows or firearms.
Misfire. Whenever you make an attack roll with a firearm, and the dice roll is equal to or lower than the weapon’s Misfire score, the weapon misfires. The attack misses, and the weapon cannot be used again until you spend an action to try and repair it. To repair your firearm, you must make a successful Tinker’s Tools check (DC equal to 8 + misfire score). If your check fails, the weapon is broken and must be mended out of combat at a quarter of the cost of the firearm. Characters who use a firearm without being proficient increase the weapon’s misfire score by 1.
Reload. The weapon can be fired a number of times equal to its Reload score. You may reload one barrel or chamber of a firearm with the Reload property with a bonus action, or all barrels with an action. You must have both hands free to reload a firearm.
Loading. Because of the time required to load this weapon, you can fire only one piece of Ammunition from it when you use an action, Bonus Action, or Reaction to fire it, regardless of the number of attacks you can normally make. (Identical to the Loading property in the PHB, reprinted here for convenience.)
Double Arquebus. The 'double' in "double arquebus" refers not to barrels (it is a single-barreled gun) but to length: it is over seven feet long, allowing it to fire farther than nearly any other weapon. Because it is so heavy--and because it takes a larger gunpowder charge than other weapons--it is typically supported with a lightweight, two-wheeled carriage, or a forked metal bipod mounted under the barrel. It takes an action to set either of these mechanisms up. The carriage can only be used to fire the arquebus while standing; the bipod can only be used while prone. If you fire the arquebus without either of these mechanisms, you have disadvantage on your attack roll, and you fall prone after the attack. A Large or larger character can fire an double arquebus without any of these restrictions.