What's the process by which the line of sight from a scope and the path of a bullet from a rifle is calibrated?

In mechanics, I studied this. Trajectory or path of the bullet is parabolic. You may read Rifle Bullet Trajectory.
Rifle shooting tips
Rifle Trajectory Table

Parts of a trajectory

The process is called Zeroing in. And nowadays some sniper have fancy balistic callculators that tell them how many clicks of the scoped they should turn.

Actually the process is called sighting.

the key is consistency. Match loads work the best so there are no fliers. Usually off the shelf ammo won’t do for serious sighting in. The trick is to get it set up to be exact at a certain distance then adjust up or down from that point by guessing the distance difference if no range finding equipment is used. Many combat scopes will have ticmarks built into the reticle to compensate distance, example the size of a man, standing, is pre calculated in a sliding scale so the shooter matches up the target size to the line in the reticle to get the proper distance. This really works if the target is standing so it became a good enough reason to not be standing out in plain sight where a sniper could draw a bead. But of course an experienced shooter will still be able to make the shot even if his target is not “cooperating”.

I’m no expert,but one can use a sight bore,start at 100 and sight it in for 50 yard increments,if you have a scope to allow for multiple ranges.

Read the book about One Shot One Kill and the part about Marine Sniper legend Carlos Hathcock and you will understand better what it takes to hit a nickle at a 1,000 yards.