Classic pseudo-constant-current method (for reference)
Using a signal generator make a circuit with the driver or device under test and a relatively large series resistor (300-1000 ohms) such that the voltage across the speaker is roughly proportional to its impedance. Calibrate the circuit with a 10 ohm resistor in place of the driver and set the output of the signal generator so the voltage across the test resistor reads some convenient value. Typically this can be something like 10mV-50mV - for the sake of this example say it is 10mV. This means that the current through the circuit is a relatively constant 1ma, and the impedance of our speaker at any frequency is simply the reading in mV. A reading of 20mV at some frequency means (by ohm's law) an impedance of 20 ohms.
The frequency is then varied to find the resonance peak of the driver in free air. This frequency is the so-called Fs, and the impedance there is Zmax. Measure the DC resistance of the speaker coil (in a quiet room - unstable readings mean the speaker is acting like a microphone) preferably to within 0.01 ohm and call this Re.
R=Zmax/Re
Find the points on either side of resonance where Z = sqrt(R)*Re. Record the frequency below Fs as f1 and the frequency above fs as f2.
Qms = sqrt(f1*f2)*sqrt(R)/(f2-f1)
Qes = Qms / (R-1)
Qts = Qms*Qes/(Qms+Qes)
Measure Vas - Test Box Method
Put the driver in a tightly sealed unlined test box of volume Vb and again measure the parameters above, but instead of calling them Fs, Qes, call them Fc and Qec, as these are done in a closed box. The box will raise the resonance, and the amount that the resonance is raised depends on the interaction between box and driver compliance.
Vas = Vb*(Fc*Qec/(Fs*Qes)-1)
Measure Vas - Added Mass Method
Add mass to the cone, ideally about equal to the Mms of the driver so that the resonance frequency is reduced by about 30%. Measure the Diameter of the radiating surface, including half of the surround, in meters. Find the resonance frequency with the added mass quantity Ma in kg - call this frequency Fsa.
This gives you the unaltered mass of the speaker diaphragm and air load in kg:
Mms=Ma/((Fs/Fsa)^2-1)
From Mms and Fs you can calculate Cms in m/N
Cms = 1/((2*pi*Fs)^2*Mms)
Adding in the diameter term, you can calculate Vas (in liters)
Vas = 1000*Cms*1.18*345^2*pi*Diameter^2/4
Using a measurement program
In practice , some amount of time spent putting the above calculation steps in a spreadsheet is useful to do briefly in order to understand the process, but in practice time is better spent learning to use a measurement program such as Speaker Workshop, ARTA, Room Equalization Wizard, etc. These programs measure the true complex impedance (both magnitude and phase) and this is useful for crossover design as well as box design.
A useful reference for parameter measurement is found in Reference 8 - Joseph D'Appolito's "Testing Loudspeakers"