#1). How? The catalogues used to contain many, many tables by manufacturers giving the correct combinations. Real simple, there are low scopes with no bell in front or small bell. 4x or less. They could be mounted with "low rings." Then came the early 3-9x with larger front bells. And "medium" height rings. Then the huge front bells that supposedly let you shoot after twilight... and some "high rings" were not high enough. You start mixing makers and you are on your own...
#2). Jack O'Connor did a magazine article that Weaver (of Tx, then) used to include with scopes. Real brief, you have three "lines" to consider.
1). "Line of bore." You look through the barrel. Straight line for all practical purposes.
2). Since you cannot fire the gun while looking thru the bore (surprise) you put reference points outside the gun, usually on the barrel and called "sights." This gives you "line of sight." Again, straight line for all practical purposes.
3). "Bullet path." Aka "trajectory." This is a curve, a parbolic curve. (accelerates as it progresses [down because the bullet is slowing in forward motion but falling as fast]) Once the bullet has left the barrel, it starts to fall. It never, NEVER rises above the "line of bore" BUT ... /THEREFORE you have to lower the rear of the barrel to point the bullet above the point you want to hit so the bullet "falls" into your target/point of aim.
Lowering the rear of the barrel causes the "line of bore" to cross the "line of sight."
And you can "sight in" for crude beginning using this first "cross." Rimfires, 12.5 yards. Centerfires, 25 yards.
The story that sticks in my head... You survey 100 yards, approx. completely level. You hang a target at say 48 inches. You return to the bench, place gun 48 inches off ground. Bore sight on bull. Exactly level. .22 Long Rifle. Load. Close action. Fire. You will find the bullet has struck 12 inches below the point of aim.
Move back to 125 yards. The bullet will strike 36 inches below point of aim. [BORE SIGHTED!]
Little crude but this is also true for .45/70 factory loads. 10x bullet weight but about the same velocity/ballistic efficiency.
SO with a .22 long rifle, you sight in to cross the first time at 12.5 yards. At 50 yards you will be about 2.5 inches high. You will hit point of aim at approx. 77 yards. And at 100 yards you will be about 3 inches low. If I remember, 15 inches low at 125 yards.
O.K. This is what the tables in the backs of reloading manuals are for. The ballistic efficiency of bullets varies with shape and velocity. You pick a bullet and "look it up." Hopefully you will have approx. velocity. [Now if you have an 18 inch barrel carbine and the data is for a 26 inch barrel... you need to do a lot of interpretation.] As I recall 150 grain pointed .30 in, say, '06... [approx. 3,000 feet per second...] hits point of aim at 25 yards. 2.5 inch high 100. 3.5 inch high at 175 yards. Hits point of aim again at 225 yards. 8 inch low at 300.
But don't take my old memory, use the tables. Bore sight in your home at 25 yards or close... then you shoot and see how far off you are. At 25 you should be on the paper. LUCK.