#1). Fire your first shots at close range to be sure you are "on the paper." Nothing quite so annoying as firing at 100 yards, walking down there only to ask "where did that one hit..." Spotting scopes save alot of walking, but firing a few at 25 yards or 10 is just too easy not too. Of course, you divide your adjustments ... 1 inch at 25 is 4 inches at 100... like that.
#2). You have three "lines" to think of. i). "Line of bore." You look through the barrel at the target. "bore sight." ii). "Line of sight." Since you cannot look down the barrel and close the action and fire the gun you look thru other reference points, sights. iii). "Line of bullet travel"/"trajectory." i). and ii). using light are for our purposes "straight lines." "iii)." is the fun one. To keep this real simple, Weaver used to include an article by Jack O'Connor to help sight in. "Rimfires" were done at 12.5 yards. In those days that meant .22 Long Rifle, High Velocity. Little else widely available. (Shorts were for sissies and girls... like that.) If you survey a strip of land 100 yards long and hang a target 48 inches off the ground, return to the bench 100 yards away, sight thru the bore with rifle "level" at 48 inches off the ground, load a Long Rifle, close the action and fire... The bullet will strike 12 inches below the point of aim. Move back to 125 yards and the bullet strike will be 36 inches low. In brief, the path of the bullet is a curve. The bullet falls from the time it leaves the muzzle and you point the muzzle above the target so it falls into the target... The recommendation was to line things up so the first point where the curve crosses the line of sight is at 12.5 yards. (Rimfires!) Then you will be 1.5 inches high at 50 yards. On again, crossing the line of sight at about 77 yards and only about 2.5 inches low at 100 yards... As I recallllllll
Point, there are tables, I know Hornady has them, in back of loading manuals that will give you the approx's for all the popular cartridges, with the manufacturer's bullets of course. Sectional density and Ballistic efficiency are involved. If you are shooting only one or two guns and with only one or two loads, it is not that challenging to memorize the "Kentucky windage" and/or adjust the scope... Some tape the information to the stock... Luck.