They may be sold in weapon shops, and also have a low chance of appearing inside crates. All Shopkeepers carry a shotgun and will use it on you if you provoke them.
A guaranteed Shotgun can be found buried beneath certain graves in Restless Dead levels with "ASH" inscribed upon them - a shout out to the Evil Dead movies - which can be unearthed using a bomb or a mattock.
Shotguns fire a scatter shot of 6 pellets (that each deal 4HP of damage) with a moderate reloading time between shots.
The pellets travel on slightly divergent trajectories and spread slightly as they travel, but this doesn't really affect long range accuracy.
If all pellets hit their mark - as is common at close range or on large targets such as a Mummy - a single shotgun blast deals 24 HP of damage.
This is enough to kill almost any enemy in the game, the only exceptions being Megamouth who has 40 HP and the Yeti King who has 30 HP - necessitating about two shots to kill either of them.
Furthermore, the final boss is immune to damage and cannot be harmed by the shotgun.
Being shot by a Shopkeeper is almost always fatal, unless you have extremely high HP or manage to avoid the majority of the pellets at long range.
Firing a shotgun produces a moderate recoil that causes the Spelunker to be knocked back slightly, which can have consequences when firing near a ledge. On ice, this effect is amplified due to lack of friction, unless you have spike shoes equipped.