Regardless the type of firearm used, or the model of the sight on it, the sight must be adjusted. It must point to the spot where the bullet is intended to strike when the trigger is squeezed. The procedure to accomplish that alignment is called “zeroing.” Because there are a few issues to consider during the zeroing of any weapon, we will examine those in an order that might make some sense.
Bullet Travel
Before we can start, we must understand that a bullet, fired from any firearm, does not travel in a straight line. Instead, it travels through space in a symmetrical open plane curve called a parabola. It will also drift laterally because of atmospheric influence and spin. To further complicate things, the line of sight is straight. Therefore, the parabola needs to be brought into alignment with the line of sight, both laterally and horizontally.

Due to the law of physics governing the flight of projectiles, if a bullet strikes the exact point of aim at 50 yards, it may not hit the point of aim at 100 or 200 yards (assuming the sights have not yet been adjusted for elevation and windage). Because of that, when claiming that a firearm is zeroed, we must specify the distances at which the sights are zeroed.
Yes, I said distances. Because the projectile will cross the line of sight twice during its flight, it is said to be zeroed at both distances. That said, most use only the farthest distance when discussing zero. Beyond that, consideration must be given to the type of firearm. Different firearms are designed to have different effective ranges. The zeroing distance depends on the type of weapon and the ranges at which it is expected to be used.
Typical examples might be pistols for defensive use that may be zeroed at 15 or 25 yards even though most pistols can be fired at greater distances. An AR-type rifle that is typically zeroed at 100–200 yards can shoot well beyond 300 yards. Typically, the zeroing distance for any firearm is the distance at which it is expected to be used under most normal circumstances.
An important consideration must be given to the manufacturer or brand of ammunition one chooses to fire. Different brands may make or use propellants that produce different amounts of energy. The profiles and weights of the bullets will also be slightly different from manufacturer to manufacturer.
All these variables affect the flight and path of the bullet. It is for these exact reasons that when the firearm is zeroed, it should be zeroed with the type and brand of ammunition that it is to be used with. When any item is substituted, the firearm must be re-zeroed with the new component, or it may not perform as expected.

Additional Factors
Another important, but overlooked, issue that affects where the bullet strikes is based on the person doing the shooting and the angle that he/she holds their head. Likewise, how they see the sights when aiming the weapon is another variable. As an example, many rifle shooters place their head so the tip of their nose barely touches the rifle stock.
Considering that different people have different shaped heads, it follows that a weapon which has been zeroed by one person will not be zeroed to the same point when another person is aiming the weapon, especially when metallic sights are used. This is not as problematic with optical sights. However, a good rule of thumb is to never let anyone else zero your firearms — except for a rough zero to get you in the ballpark or more precisely, “on paper.”
Another area of consideration must be the condition or wear and tear of the firearm, it may shoot differently after some use, due to wear of the rifling, chamber, etc. Rough usage may also misalign the sights. Hence, all weapons may need to have their zero checked and readjusted after some use. Additionally, with rifles used for accurate shot placement, the zero needs to be reconfirmed and possibly adjusted when changes in altitude or temperature take place.

With that said, I will explain a procedure to zero basic adjustable iron sights on a handgun and a commercial AR-type of rifle. The same basic principles can be used for zeroing any type of pistol or rifle with any basic type of sight.
As a point of information: The U.S. Army and U.S. Marine Corps advocate the reference distance for zeroing the rifle to be 300 meters. However, the actual procedure is done at 25 meters. To accomplish that, they use a target that has everything scaled by 1/12 actual size. This is also a procedure that you can use to get everything ‘aligned and true’ before moving to 100 yards (or farther for rifles) to confirm their zero at actual distance.

It must be remembered that with military rifles, the rear sights are adjusted in discrete incremental amounts. Each time they are adjusted by one increment, a clicking sound is heard. Hence the expression for adjusting sights by a specific number of clicks. It must be noted that on some M16 and AR-style rifles, the front sight is also adjustable for elevation.
Windage Adjustment
Before you start the sight-in process with any firearm, you want to establish and set the firearm to its ‘mechanical zero.’ This is accomplished by adjusting the windage knob. Therefore, the windage indicator is centered on the windage scale, and the elevation knob is set at 100. The procedure will vary for different types of sights. Refer to your firearms user manual for instructions on how to accomplish this with your specific firearm.
New optical sights normally ship from the factory set at their mechanical zero. It is assumed for the purposes of this article that the reader either knows how to correctly install or mount their chosen sighting system or has engaged the services of a competent gunsmith to properly complete the procedure.
The next step is to take the firearm to the range and placed it on a firm base, such as a solid shooting bench with sandbags or appropriate pistol or rifle rests that reduces human error. At this point, it is important to know the correct point blank distance for the gun and ammunition combination you will be shooting. Point blank is that distance where the projectile crosses the line of sight. It will do that twice but you must know the first or closest distance that will occur so you can set the target at that distance. (For reference, please see the provided illustration.)
To determine the point blank distance, you must know the trajectory of your load. Point blank distance can be computed with a ballistic calculator to get approximate distances (once you know your muzzle velocity). Of course, everything must be confirmed by shooting at actual distances.

With a rifle, you can determine the maximum effective range, which will give you the point blank distances. Pick the first point of intersection as the one to set your target at. For a defensive handgun, 25 yards is considered the standard. However, you can use 15 yards if you are more comfortable shooting at that distance. For rifles with optical sights, it’s imperative for you to know the exact height of the sights above the bore to compute the point blank distance. It can work out to be anything from 24–50 yards for most normal platforms and loads.
Defensive Handguns
For illustrative purposes, let us look at a handgun to be used defensively first. Once everything is set up, make some notes to keep track of the details. I keep a notebook and record the date, firearm, load, distance, temperature, lighting conditions, and wind speed and direction. From a solid rest, I fire as precisely as I can — three slow shots. Normally, I would fire five shots to eliminate operator error. However, during this time of ammunition shortages and high prices, three will do.
I will note the distance of the point of aim, order of hits, and size of the group. I then triangulate to determine the center of the group. Next, I adjust the sights to a determined number of clicks. This adjusts the point of impact to the point of aim. I let the firearm cool until the barrel is cold to the touch. Then, I repeat the process until the point of aim and point of impact coincide before I call it done.

Always remember, accuracy is affected by temperature, altitude, vibration, shock, rough usage (i.e., the sights get knocked out of alignment), barrel cleanliness, etc. It’s necessary to check and re-zero the weapon periodically or whenever a major environmental change takes place. How often this is done depends on the user and how much accuracy you expect from each particular firearm. For example, defensive pistols have different requirements on how often to recheck zero than rifles that are expected to hit prairie dogs at 1,000 yards.
As the Colonel used to say, “Ride hard, shoot straight, and speak the truth!”

I agree with Col K. I usually build a ballistics “cheat sheet” on every hunting round I am shooting. They are roughly about credit card size to make them easy to laminate and fix to the stock of the guns with wooden stocks. I do almost all of my sighting in at 25 yards using those cheat sheets. Depending on the caliber, I calculate what zero I will use. My .270, with a 250 yard zero, will be 0.7 inches below at 25 yards ; this gives me roughly a 6 inch point blank range out to 300 yard, where It will be just under 3 inches below line of sight and at 400 yards it’s 12.7 inches below. My 6.5 Swedish has a 300 yard zero due to its iron sights, and at 25 yards is 1.4 above, and will be 6.1 inches above line of sight at 150 yards . My SKS is set for a 200 yard zero. At 25 yards it is 0.6 inches below and its highest point above line of sight sitting at 2.7 inches high at 125 yards. My AR has a 200 yard zero; at 25 yards it is 1.6 below and its highest point is between 125 and 150 yards at roughly one inch above. I don’t try to take deer beyond 150 yards with either my SKS or the AR because I don’t like the energy numbers at those ranges. With the Swedish and my .270, I am only limited by what I can see with the sights or optics. I have taken multiple deer at ranges of 400 yards plus. I always use my range finder on deer that appear to be 100 yards or more if I am hunting in an area that I haven’t already ranged landmarks.
Col K is right on point. In fact when ammo ballistics is known a 25 yard zero is all that is needed with glass. One can then adjust for no wind range by adjusting for known or expected rise or drop. Zero for hunting should be set in advance for typical shot distance for the sought after game. It has worked for me just fine.
Every time a person goes into this subject they do exactly what you did. Fills a page or two trying to explain it and show how knowledgeable they are on the subject.
For once I’d like to see some one use just as few wods possible to get to the point.
Show a target with an impact point and use a simple drawing or representation to explain which way to move a rear or front sight left or right to correct it to center. As the same with elevation, up or down. This should also be done for glass too.
Just keep it simple. Would be far less boring and a lot easier to focus on.
I strongly recommend every shooter make their initial sight-in at close range, then verify and tweak it at long range. Here’s why. I recently used a 25 meter target to zero an early model AR with A1 iron sights. I ended up moving the rear sight all the way left to get the shots centered. Had I tried doing this at 100 meters, imagine how many rounds I would have expended just trying to hit paper.