The neck of a guitar is the part a guitarist has the most contact with. It ends up playing a large role in the comfort of a particular guitar. Getting the correct measurements is crucial when it comes time to order a replacement guitar neck or specify a new custom guitar neck to get the right sized neck. It is very easy to neglect crucial measurements, but taking the time to be thorough will avoid those issues.
Measure the scale length. If the neck is still attached to the guitar body, this is the distance from the nut to the bridge. Otherwise it is twice the length from the guitar nut to the 12th fret.
Measure the fretboard width at the nut, 12th, 21st, 22nd and 24th fret. Different companies and luthiers will use different references, which is why all four of those measurements are useful to have.
Measure the thickness of the neck at the nut and 12th fret. This measurement is from the top of the fretboard to the back of the neck, do not include the height of the fret.
Measure the fret height. This is the height from the top of the fret to where it touches the fretboard; do not include the part of the fret that is below the wood surface.
Determine the fretboard radius. This measurement is very difficult to measure precisely. It is far easier to reference the standard for that type of guitar.
Most guitars should have a 24.75 or 25.5 inch scale. There are guitars with different scale lengths, but double check if you get a different value.