Most guns come from the factory with some kind of pre-installed sighting system; with pistols and rifles, this usually comprises one sight at the end of the barrel, and one closer to the shooter's eyes. These are usually called "iron sights," and although they can have different configurations, they all function more or less the same way. With shotguns, this usually is a "bead" at the end of the barrel. Although most guns can have optical sights--scopes and reflex sights--installed later, it's important to understand how to use your gun's iron sights. Your NRA has put together a comprehensive guide to using those factory-installed iron sights.
The most important thing to remember is to focus on the front sight, the one that's at the end of the barrel. That might seem a little counterintuitive, but it's 100% reliable because it harnesses the way human eyes work. The best way to hit what you're aiming at is to make sure that the front sight is in sharp focus, and everything else is just a little blurry.
Shotgun shooting is actually a little different, particularly if you're "wingshooting." Wingshooting is simply the act of firing at a moving target, such as a flying duck or a clay target. If you're doing that, you should actually be focusing on the target.
However, frequently shotguns are used to shoot at more-or-less stationary targets, as in turkey hunting. In this case, you use "rifle rules" to aim your scattergun. Of course, there's plenty more to know, and your NRAFamily.org has it all right here.