http://www.civilwarartillery.com/books/robertshandbookofartillery.htm
Aiming Ranging was done mostly with lookup tables, although I suspect experienced officers would learn to eyeball it. There is a table in Roberts Handbook I was unable to link because formatting isn't easy in Reddit. It gives elevation, range, time of flight and length of fuse for a Parrott Gun, in this example.
Edit: Ranging, dammit. Not aiming.
Here is some turgid prose on the issue.
How is the elevation or depression given? The elevation or depression, which depends upon the charge, the distance, and the position of the object above or below the battery, must be ascertained from tables or by experiment, and the proper degree given by means of instruments.
When will the object be struck by merely directing the line of metal upon it? But in one case—when it is at point-blank distance.’
How must the line of metal be directed for all ranges less than the point-blank range, in order to strike it? So as to pass below the object.
Give a simple rule for firing at objects within point-blank. Add to the point-blank range the difference between it and the required range, set the scale to the elevation corresponding to this sum, as shown by tables of faring. Then aim the gun directly at the object; now apply the scale, and observe where the visual ray of the scale strikes the ground, and having noted this point, aim the gun directly at it.
How must the line of metal be directed for ranges greater than the point-blank range, in order to strike it? Above it.
When the line of metal passes over the object, what instruments must be employed for giving the proper elevation? The gunner’s quadrant, or the breech-sight.
How is the quadrant used? After the direction has been given, the quadrant is applied, either by its longer branch to the face of the piece, or this branch is run into the bore parallel with the axis, or it may be applied to the upper surface of the lock-piece, making the allowance due to its inclination with the axis of the piece, which ought to be previously determined, and the elevating screw turned, or the quoin adjusted, until the required degree is indicated.
How is the breech-sight used? It is first set to the elevation corresponding to the distance; it is then applied to the highest point of metal on the base-ring, and by the elevating screw, or quoin, the notch of the breech-sight, the highest point on the swell of the muzzle, and the object, arc brought in the same line.
What is a line thus determined called? An artificial line of sight.
In the absence of instruments, how may the elevation be given? By placing one or more fingers of the left hand upon the base-ring, perpendicular to the axis, and using them as a breech-sight. NOTE.—In practice, it is well to fire two or three shots to determine the range experimentally, as it is affected by divers causes.
Should the line of metal be always directed in the vertical plane passing through the object? No; as in practice there are circumstances (as, for instance, a strong wind blowing across the field of fire) which will cause a ball to deviate from this plane, it follows that to strike the object, in such a cane, the line of metal must be directed to its right or left; the gunner judging of the distance by observing the striking of the shot.