Rim Measurements
ERD
ERD is complicated because it is not an absolute measurement of the rim, but is rather a measurement of where the wheelbuilder would like the ends of the spokes to be. This can vary with different types of nipples and where the wheelbuilder wants the spoke to end in the nipple.
Freespoke strives to always gather the ERD in a standardized format, because it is quite easy to apply a correction to the ERD or calculated spoke length to support builder preference or the use of unusual nipples. The standard used by Freespoke is with the spoke end flush with the bottom of the screwdriver slot in a standard 12mm DT Swiss nipple. (Wheelsmith and Sapim and similar nipples almost always have a negligible difference and can be considered interchangeable)
My preferred measuring system is simply two new and unbent spokes, cut to known lengths with the cut ends ground square and flat. The threaded ends are treated with loctite and threaded into two new DT 12mm nipples until the ends are exactly flush with the bottom of the screwdriver slot. Precision matters, because any error in length or positioning of your measuring spokes will affect the resulting calculated spoke lengths by nearly a 1:1 ratio. I use a pair of 300mm measuring spokes as well as a pair of 250mm and 200mm spokes to make it easier to work with small rims. I use brightly colored alloy nipples to make them less likely to be accidentally discarded, since they look a lot like spokes cut out of a scrapped wheel at first glance.
Measuring with these spokes requires only a decent small metric ruler and a good eye. Insert the spokes into opposite holes on the rim, ensuring the nipples seat fully and are not bound up. With the rim laying flat on a work surface, pull the two spokes lightly towards one another, pivoting them in space until you can see that they are parallel with one another. I hold the ruler beneath the overlapping spokes by pinching one spoke and the ruler with one hand, and steering the second spoke with the other hand. Rather than using the zero point (end) of the ruler, simply line up any 10 line with the end of the spoke pinched with the ruler. Measure the overlap by simply counting tens and ones of millimeters on the ruler, swinging the two spokes slightly to help make sure the spokes are as parallel as possible (resulting in the longest overlap or shortest resulting ERD).
A few manufacturers make ERD measuring tools, but I don't have firsthand experience and don't know how their resulting numbers will compare to this system. You are free to use any measuring system you can derive, so long as you are sure it can reproduce the same numbers as this system, or your numbers can be offset by a derived value to result in a measurement that matches this system.
You might notice that even if you take extremely careful measurements, the ends of the spokes usually end up slightly past the bottom of the screwdriver slot. Bear in mind that the calculated spoke length is a theoretical 3D path, and does not inherently factor in spoke stretch, the effect of spokes being all heads-in/heads-out, whether the crossing spokes are interlaced or not, how much chamfer the hub flange holes have, how long the elbow section of the spoke is, etc. If you find a calculation really far off, the error is almost always in the part measurements, especially ERD, which affects spoke length on a nearly 1:1 ratio. Some values have very little impact on spoke length, such as center-to-flange distance. Some values can have a highly variable impact, such as flange PCD affecting spoke length 1:1 for radial lacing but almost not at all for near-tangential lacing.
Offset Drilling
This is the distance from the centerline of the rim to the center of the spoke holes. Freespoke allows left and right values to be handled independently, since not all rims have their spoke holes all in the same plane. This is simplest to measure with the rim laying flat on a good flat work surface. Measure from the work surface up to the eyeballed center of a rim hole, then subtract this value from half of the rim outer width. For example, if you measure 10mm from table surface to center of spoke hole, and the rim is 25mm wide, the math is (25mm / 2) - 10mm = 2.5mm. Note that a positive value indicates right holes more to the right of center, or left holes more to the left of center. If the spoke bed is offset but all in one plane, the values will be the same except one will be negative and one positive. For a rim with holes staggered across the centerline (many fatbike rims), both values will be positive. Two negative values would be highly unusual, and would indicate that the left and right spokes cross the centerline of the rim. I think this is used on a few BMX rims, but that's probably it due to the extreme angles that can quickly result.
Outer Width
Ignore angled or curved profiles and measure squarely across the widest point of the rim's cross section. A caliper will give the best results. Desired measurement accuracy is 0.1mm, but I recognize that variation in manufacturing will usually result in parts that vary by a few tenths of a millimeter.
Note that many rim manufacturers advertise a width of their rims, and these stated values are commonly inexact. Sometimes, as is common with tires, manufacturers will intentionally state a wider than actual width in order to help have "the lightest 28mm rim" or some such nonsense. Needless to say, real-world accurate measurements are greatly preferred.
Inner Width
Measure across the narrowest gap between of the hooked walls of the rim. Use inside jaws of a caliper.
Overall Height
Measure the vertical profile of the rim extrusion, not including eyelets or other non-continuous protrusions.
Brake Wall Height
On rim-brake-compatible rims, measure the height of the flat braking face, not including any curved portions at the edge transitions. This will definitely involve some variation from manufacturing, but is helpful to generally identify wide vs narrow brake walls. Resolution to a half millimeter is a good goal.
Hub Measurements
OLN
The over-lock-nut dimension (also sometimes abbreviated as OLD) is the same as the inner spacing of the dropouts when the wheel is installed. This will usually be one of the common values of 100mm, 120mm, 126mm, 130mm, 135mm, etc. Please ignore slight deviation and use the intended standard (a hub with an actual measured OLN of 134.9mm will simply be entered as 135mm)
For unusual scenarios such as Lefty hubs and trike hubs, there is not a clear OLN and text labels are currently not supported. In the case of Lefty hubs, please measure them while installed in the official Lefty truing stand adapter that effectively converts the hub into a 100mm-spaced front hub.
Flange PCD (Pitch Circle Diameter)
Often referred to as simply flange diameter, this is technically a measurement of the PCD of the holes drilled in the hub flange. This is a linear measurement from the center of a hole to the center of the opposite hole on the other side of the same flange.
Rather than trying to measure center to center (and eyeballing both center points, introducing two sources of error), measure from inside to outside of the same holes. Hook one of your caliper's outside jaws in the first hole, and eyeball the other jaw parallel to the opposite wall of the second hole.
Alternately, you can measure inside-to-inside and add one hole diameter, or measure outside-to-outside and subtract one hole diameter, depending on where your caliper jaws can most easily reach the holes without being blocked by the hub shell and axle.
Center-to-flange offset
This is the distance from the center of the hub (midpoint between the locknut faces) to the midpoint of the flange holes in question. (not to the inside or outside face of the flange!) This is very difficult to measure directly, and it is much simpler to measure the flange offset from the locknut face, then subtract this from half of the hub's actual OLN measurement. Rest the locknut face squarely on a flat and true edge such as a metal countertop edge. Use a ruler or caliper depth probe to measure from the straightedge face to the midpoint of the flange (eyeball the midpoint). If this is 23.5mm and the hub's actual measured OLN is 100.2mm, the math would be (100.2mm / 2) - 23.5mm = 26.6mm. Error in this measuerement will have very little impact on the calculated spoke length since the bracing angle of the spokes is a very shallow angle. Desired measurement precision is to a half millimeter.