The way that spectrum analyzers are built is typically to use
calibrated attenuators and linear gain stages that have very low
distortion (and similarly low "compression"). Then it becomes a matter
of determining the voltage after amplification. They do NOT use AGC
voltage, or at least not anything like the AGC used in a typical ham
receiver. The way we do it here is to digitize the RF signal and do
some appropriate digital signal processing on it (e.g., FFT) to display
the spectrum and to calculate amplitudes and band powers and the like.
Modern digitizers are very linear indeed and can be used to measure
signal amplitudes over a range in excess of 120dB with relative
accuracy far better than an S meter over most of that range, and still
considerably better even at the bottom end of the range. It doesn't
even take a huge number of bits in the digitization to do it; consider
that a typical delta-sigma ADC is a one-bit converter followed by lots
of processing gain.

The way it can be done "on the cheap" is to use a calibrated attenuator
and a single known signal level. Then you compare your known signal
level with the unknown, adjusting the attenuator to bring your
(typically large) signal down to the same amplitude as the unknown.

For S-meter levels of accuracy, linear non-AGC'd stages feeding one of
the RF power detectors from Analog Devices, Linear Technology or others
will work fine. Most of them have an output voltage proportional to
the log of the input voltage, and so can be calibrated to read dB
linearly on a linear meter scale. If your receiver has a good front
end, it shouldn't need AGC up through the filter following the mixer,
and you could pick off there after the filter to drive the meter
circuit. That seems overkill, but it would get you a _good_ S-meter.
Then you'd have to calibrate out the front-end gain at least per band,
assuming you have at least some front end filtering that doesn't have
the same gain (loss) on each band.

Field strength meters that accurately measure an RF electromagnetic
field are basically spectrum analyzers fed by calibrated antennas.

That may be beyond what you wanted to know or do, but it should give
you a pretty accurate picture of how modern commercial gear actually
does make RF voltage measurements. You could add calibration (for
absolute amplitude accuracy as well as spectral flatness) to all that
as a whole 'nuther topic, though. For example, the amplitude
characteristics of any filters the signal passes through in the
spectrum analyzer must be properly accounted for, as must temperature
drifts in instruments with high accuracy.

Cheers,
Tom