Elemental Firearms

Elemental Firearms were an invention created by the western branch of House Cannith in their efforts to find a product that could be produced quickly and that would help the house in the midst of their financial troubles. The designs were quickly copied by the other Cannith houses, and shortly thereafter by other factions.
The core design binds a small elemental spirit (typically a mephit), trapped in a dragonshard, into a magic weapon that uses the elemental's energy to propel a slug or pellet. The user must attune to the weapon in most cases (it is rumored that some black-market versions are available that don't require attunement), and the weapon is "powered" by a connection that is formed between the user and the elemental.
One of the primary advantages of these weapons is that the slugs are far easier to produce and transport than arrows or crossbow bolts. The slugs carry with them energy derived from the elemental that fires the weapon and a faint imprint of the personality that is attuned to the weapon, which can be detected with an identify spell if the slug or a fragment of the slug is recovered.

Proficiency

Elemental firearms are considered martial weapons. In addition, characters who are proficient with some crossbows are proficient with some elemental firearms.

• Proficiency with Hand Crossbow includes proficiency with elemental pistols
• Proficiency with Light Crossbow or heavy crossbow includes proficiency with elemental rifles

A variation on the Crossbow Expert feat, called Elemental Weapon Expert is available in D&D Beyond: Elemental Weapon Master

Priming

To fire, an elemental firearm must be primed, which involves holding the weapon and speaking its name or command word -- which can be set when the weapon is attuned. This requires an action, a single attack in a multi-attack, or a bonus action to perform. Once the weapon is primed and able to fire for one minute, unless it is dropped or holstered, or in some other way the direct physical connection between the user and the weapon is lost.
The original, and still most popular designs, were single-shot pistols and rifles, which are relatively common because of their use in the militaries of the Galifar nations, among others.

Weapons

Weapon	Cost	Damage	Weight	Rarity	Properties
Cannith Elemental Pistol	100 gp	1d6 piercing + 1d4 acid/cold/fire/lightning/thunder	3 lb	common	ammunition (range 30/90), elemental crit, loading, priming, misfire 2
Cannith Elemental Rifle	200 gp	1d8 piercing + 1d6 acid/cold/fire/lightning/thunder	5 lb	common	ammunition (range 60/240), elemental crit, loading, priming, misfire 2, two-handed

House Cannith has produced a few more advanced models and packages. A Palm pistol is a very small weapon that is easy to conceal. A pepperbox is a six-barreled version of the pistol which allows for the user to fire more shots before needing to reload.
Other factions have also started to produce their own variations on these weapons. The Church of the Silver Flame has created their own holy version of the pistols using Flame-touched Iron and divine power, while the Karrnathi military has commissioned a necromantic version to arm their skeleton musketeers, powered by a ghost bound to the crystal. The Yuan-ti have designed a variation on the design that fires a stream of poisoned needles fired by an air mephit.

Weapon	Cost	Damage	Weight	Rarity	Properties
Cannith Elemental Palm Pistol	200 gp	1d4 piercing + 1d4 acid/cold/fire/lightning/thunder	2 lb	uncommon*	ammunition (range 30/90), concealable, elemental crit, loading, priming, misfire 2
Cannith Elemental Pepperbox	600 gp	1d6 piercing + 1d4 acid/cold/fire/lightning/thunder	3 lb	uncommon*	ammunition (range 30/90), elemental crit, reload 6, priming, misfire 2
Cannith Elemental Brace (2 matched pistols, attuned as one)	250 gp	1d6 piercing + 1d4 acid/cold/fire/lightning/thunder	6 lb	uncommon*	ammunition (range 30/90), elemental crit, loading, priming, misfire 2
Silver Flame Peacemaker	200 gp	1d6 piercing + 1d4 radiant	3 lb	uncommon*	ammunition (range 30/90), radiant crit, loading, priming, misfire 2
Karrnathi Reaper	200 gp	1d6 piercing + 1d4 necrotic	3 lb	uncommon*	ammunition (range 30/90), necrotic crit, loading, priming, misfire 2
Yuan-ti Needler	150 gp	1d6 piercing + 1d4 poison	3 lb	uncommon*	ammunition (range 30/90), poison crit, loading, priming, misfire 2

*rarity is used in this case to indicate the relative cost to buy and make these weapons, and how they compare to other magic items available in Eberron, and is not an indicator of their relative availability for sale in most settlements. Versions with further enchantments (+1 to hit and damage, etc) are also available.

Properties

Ammunition, loading, two-handed: as in PHB
Concealable - Perception or investigation checks to detect this weapon are made with disadvantage (-5 to passive checks)
Elemental Crit - When you score a critical hit with this weapon, in addition to the extra damage from the critical (doubling both damage dice) there is an additional critical effect based on the elemental bound into the weapon.

• Acid - Acid continues to burn the target, doing another 1d6 acid damage at the start of the target's next turn
• Cold - the target's movement speed is reduced by 10 until the end of their next turn
• Fire - The target catches fire, and is burning, suffering 1d6 fire damage at the start of each turn until they or an ally spend an action to put the fire out.
• Lightning - The target is stunned until the end of their next turn
• Thunder - the target is deafened for one minute.
• Radiant - the target is blinded until the start of their next turn
• Necrotic - the target cannot recover hit points until the end of their next turn
• Poison - the target is poisoned until the end of their next turn.

Priming - an Elemental weapon must be primed for use by holding the weapon and speaking its name or command word (set when the weapon is attuned, or when the weapon is created for those rare examples that do not require attunement.). The priming lasts as long as the weapon is held and the user is conscious
Misfire Whenever you make an attack roll with an elemental 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 must be re-primed to be used again.
Reloading # - The weapon can be fired a number of times equal to its Reload score before you must spend 1 attack or 1 action to reload. You must have one free hand to reload a firearm. 
Dangerous Misfire - When this weapon misfires, roll a d20. On a 10 or less, the device explodes, doing 3d6 (elemental) damage to the wielder and destroying the weapon.

Understanding how Priming/Loading/Reload all work together

The Priming feature of the elemental firearms is essentially something similar to turning the power on so that the weapon can be used.  The weapon's prime can be lost in the case of a misfire, which then will require re-priming to get the weapon shooting again.  But, in general, you can prime the weapon once and get shooting.  
The Loading property, from the PHB and as we will use it here, has a very specific impact. It limits a weapon to a single shot as part of an attack action for weapons that have the Loading property.  So, for example, a crossbow doesn't require any sort of extra action to shoot, but the mechanics of shooting it make it difficult for someone using a crossbow to make a second shot with the crossbow in the same attack action (for characters who are able to make two attacks with the same attack action).  
So, elemental weapons with this property have the same limitation.  You don't need to spend any sort of action to load them, but you can only take one shot per attack action.  
A character who would like to be able to fire a weapon more than once per attack action will need to consider one of the more advanced versions of the weapons that has the "Reload #" property instead of the loading property.  
The "Elemental Weapon Master" feat makes it easier to prime (it can be combined with the free action to draw the weapon), it allows two weapons to be attuned with a single attunement slot, and it allows a character who makes an attack action with a one-handed weapon to make a bonus action attack with a one-handed elemental weapon. So that means:

• Make an attack with a one-handed weapon (like a short sword) and then make a bonus action shot with the elemental firearm
• Make an attack with a one-handed elemental weapon as an attack action, then take a second shot as a bonus action with the same weapon (or a second elemental weapon in an off-hand).  
• In either case, if the character has a weapon with the loading property in each hand, they won't have a free hand to reload the weapon for a subsequent attack, but they'll be able to get off a second shot.