I know that from nose to tail the aircraft is divided by STA (station). At least for Boeing and Airbus this is the case but I am not familiar with other manufacturers. However, there is also two other dimensions that give every location of an aircraft an identifiable point location. It's obviously not x,y,z. What is this coordinate system and approximately what does one unit along each access mean in terms of inches or centimeters?
Stations (STA), generally Fuselage Stations (FS), designate location along the length of the aircraft, increasing from nose to tail. Generally station 0 is somewhere in front of the airplane. One reason for this is that if the airplane grows longer, there still won't be any negative stations, and sections of the plane keep their station numbers. FS 100 can also be placed at an important location (looks like the firewall below).
Water lines (WL) designate location in the height of the aircraft, from ground up. You can probably guess by now that these are holdovers from the marine industry. Like the stations, water line 0 is generally a bit below the aircraft, possibly to have WL 100 at the center of the fuselage, or WL 0 could be at the bottom of the fuselage.
Butt lines (BL) designate location left/right on the aircraft, generally centered in the middle.
While the main system is based on the whole airplane, different parts (like the wings) have their own system of STA, WL, and BL.
The stations are generally in whatever unit is being used for the aircraft. In the US, this is inches.
See this link for an example and further explanation.
For a picture similar to the one below but with more detail, see here.
There is a fair amount of variability between aircraft manufacturers as to how they reference physical locations on their airplanes, especially along the longitudinal axis. Even within a company, different schemes are sometimes used for different models.
For example, on the Boeing 747-100, -200, -300, and -400 aircraft, the reference datum is 90 inches in front of the airplane's nose. Why 90? Because the tip of the 90 inch test probe for pitot tube calibration on the original aircraft was the zero point.
However, for the 767-300 the reference datum is 28.5 inches aft of the airplane nose, which of course means that weight and balance calculations have to deal with negative arms.
Boeing uses two systems to refer to a longitudinal axis location. The Boeing Weight and Balance Control and Loading Manual puts it like this:
Balance Arm (B.A.) A true measure of distance from foward to aft, in inches, from a fixed datum. The fixed datum is selected by the airplane manufacturer. Balance Arms are used in weight and balance calculations.
Body Station (B.S.) A manufacturing location on the airplane. For first of an airplane model, B.S. are continuous from the front to the aft of the airplane. For later versions that are either stretched (i.e. fuselage inserts added) or shrunk (i.e. fuselage sections removed), B.S. becomes discontinuous, for manufacturing reasons.
Another system for referencing a point along the longitudinal axis is the percent of the mean aerodynamic chord (%MAC), and to the best of my knowledge this is standardized. C.G. limits for the various operating envelopes (zero fuel weight, taxi, takeoff, landing and others) use the %MAC for the x-axis and weight for the y-axis. Thus, weight and balance calculations come up with the actual C.G. in, say, inches, and then translate this to %MAC for to see if the C.G. lies within the the operating envelopes. The calculation is straightforward. Take the C.G. in inches, subtract the leading edge of the MAC, divide by the length of the MAC, and multiply by 100.
Note that for purposes of C.G. calculation, the wings have to use the same reference system as the fuselage (or have it translatable in reference to the fuselage) because the C.G. of fuel tanks varies depending on how much fuel there is.
Typically wide-body cargo aircraft have lateral imbalance limitations, and for that the lateral referencing system is used. For the 747-400, for example, the maximum lateral imbalance is 10,000,000 inch-pounds up to 846,000 lbs. From there it slopes to 3,340,000 inch-lbs at 913,000 lbs.
It is much different with depending on what you are doing. Engineering drawings reference a 3 point system for installations mainly Station (X or FS), Butt Line (Y or BL), and Water Line (Z or WL) these 3 coordinates dictate where things are installed exactly. If you were to look at the production drawings of those light piston and corporate aircraft you would see these much like the illustrations given by Fooot above.
As you are maintenance, simplified drawings are issued to expedite work. It's much easier to tell you it is Fwd of INBD flap rail than FS XXX, LBL YYY, WL ZZZ, as a technician would be more familiar with the location of the INBD Flap rail than its coordinate location.
If you were building that plane, the coordinate locations would be given as it would have to put in an specified location to comply with the type certificate of that aircraft at least in America.
To my knowledge there isn't a coordinate system to describe locations on an aircraft airframe. Measurements along the longitudinal axis of the aircraft exist for center of gravity measurements. These measurements are made as an "arm" measurement from a standard arbitrary point, known as the datum. Specific measurement locations are "stations". There is no real need as far as I know to have a measurements in the other 2 axis.
For locating components for maintenance purposes, my experience of technical manuals usually describe locations verbally, such as "the flap actuator can be located forward of the inboard flap rail".
My experience is mainly with light piston aircraft and corporate jets, it could be different with larger aircraft.