A great many rifles come from the factory with "iron" sights, and learning to use these is a valuable skill. However, for extended ranges, or folks with bad eyes, these basic sights fall short. They're also usually only minimally adjustable, if that. These factors combine to push us to seek out better sighting methods.
There are two basic categories that cover these better methods. The first, and the focus this week, are traditional magnified riflescopes. The second, and next week's focus, are modern electronic sighting systems.
A scope consists of two lenses in a sealed metal tube. On one of the lenses, the various lines and marks used to line up your shot are etched. Depending on tube length and lens characteristics, scopes can provide magnification from 1x to 24x and beyond. Higher magnification makes it easier to see and identify your target, but the higher the magnification, the narrower your field of view.
While some scopes have a single, fixed magnification, the vast majority sold today have an adjustable range of magnification to allow more versatility. For the vast majority of uses and users, 3-9x is plenty of magnification without having too narrow a field of view.
Speaking of field of view, many scopes with a millimeter measurement, such as "3-9x magnification, 40mm lens." All other things being equal, wider lenses are generally better as they offer you a larger field of view at higher magnifications. There are other mathematical reasons for this "bigger is better" rule, but it is enough simply to know that this is true.
While it is true that quality in scopes goes up with price, most folks derive little to no real benefit from a scope that costs more than some cars I've owned. The real winners in the budget scope department are the Burris Fullfield and things made by Vortex. I've been particularly happy with the Vortex Crossfire.
To mount your optics, you want rings that are solidly made, with multiple tensioning screws. It is usually just fine to go with what your gunsmith or gunshop recommends, and worth it to let them mount it and roughly sight it in for you. You'll still need to make fine adjustments when you actually shoot the gun, but they can get you close and save you substantial time.
Next week, we'll look at the fancy modern electronic optics.