I've noticed a recent rise in popularity of the shotguns. However, I haven't found any good resources on the basic mechanics and how to properly utilize shotguns. Most people's knowledge of shotguns is "Play close angles." and it ends at that.

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AIMING WITH SHOTGUNS

However, I have seen people complaining about how they seem to be playing at the proper range, but their shotgun seems to do no damage despite this. The main issue is that they're treating the shotguns like traditional rifles, and they're pretending that the center dot in the shotgun is their crosshair. It usually ends up looking something like this:
https://imgur.com/a/zdTzwkH

However, shotgun pellets are spread randomly throughout the circle, and about half of the circle is going to hit nothing but air.

Instead, you should try to have the top of the circle over the top of the enemy's head so that the amount of pellets that will hit will be maximized. It will end up looking something like this: https://imgur.com/a/qZe3su9

If you're struggling to understand this, a good comparison is Jett's ultimate. When you right click, or basically shotgun all five knives, you usually end up aiming towards the body to try to maximize the number of knives that hit your enemy. Even though headshots end up getting you more damage, even if your aim is perfect, you could get unlucky and completely whiff a shot that looks "directly on" your opponent.

CROSSHAIR PLACEMENT

Crosshair placement with shotguns is something that is difficult to get used to, as you are trained to keep your crosshair (or the center of your screen) at head level, and many higher level players will instinctively know approximately where their crosshair is without actually looking at it. It's why players are able to play without a crosshair and actually perform relatively well. If you're a higher level player it will be very hard to try and switch to shotguns and utilize them properly without explicitly thinking about it.

Your crosshair should be a lot lower than it usually is when it comes to shotguns. A rule of thumb I use (that doesn't really apply at longer ranges, but then again, you should avoid those at all costs when using shotguns anyways) is that the very top of the circle should be a little above where my crosshair would be with a rifle.

There is no real universal rule for crosshair placement with shotguns as far as I know, but after a while you get a vague feeling of where your crosshair should be.

POSITIONING (AND UTILITY)

Kaemi and Quarkwy (aka Shotgun Sage) have some good guides on positioning and where to play. You should play around 0-15m(you can go up to 20, but it will probably be a 2 or 3 shot with the bucky) away from your opponent when you have a bucky. Try and avoid long range encounters and force/create short distance engagements by using utility. The most obvious example of this would probably be Jett's movement abilities. Her dash and updraft can make her very unpredictable and allow you to get close to your enemy very quickly. For somebody like Sage, you use slow orbs so that you can push closer and close the distance while they are unable/unwilling to push/peek because of the slow. You also use her wall in order to reposition or get off angles to surprise your opponents.

I won't go too in depth on this topic because there are already good resources and good ways to learn how to position and use utility properly, and it is also fairly intuitive.

TL;DR

The entire point of using shotguns is to be unorthodox and unpredictable, and to surprise your opponents. You can't just pick up a shotgun and play exactly the same as somebody with a rifle would. Shotguns also have many fundamental differences to the rest of the guns in the game, and you have to learn a whole new set of basic mechanics. You have to change a lot about your playstyle and mechanics, and force yourself to play around the shotgun instead of expecting it to magically change itself for you.

This may make it seem like shotguns are bad and shouldn't ever be touched. Something important to note is that your opponents have to play around your shotgun as well. Many people will get tilted/rage and fail to adapt, calling shotguns a "no skill gun" and simply flaming you in all chat. If they fail to adapt, and you play shotguns properly, you should be able to perform well with shotguns, sometimes even better than you would with normal guns.