There are a number of approaches. The three workable approaches would be:
- Use a device called a "digital pot"; these behave electrically much like real pots, provided that all three terminals remain between the voltage rails. Note that many digital pots have fairly high wiper resistance, and fairly crummy resistance tolerance, but pretty good resistance matching; they are often used in cases where they are driven by low-impedance sources, and they are used to feed high-impedance inputs, so the exact resistance characteristics don't matter.
- Use a scaling digital-to-analog converter which can accept the analog signal as its reference. A scaling DAC behaves something like a digital pot which has one end tied to physical or virtual ground. The fact that one end is "tied to ground" may simplify the circuitry compared to a digital pot.
- Use an analog-to-digital converter to convert all incoming signals to digital form, then process them digitally (doing things like scaling them up and down by multiplying the numbers), and then output them all using a digital-to-analog converter.
- If the signal originates in digital form (as with a CD player), do processing including the volume adjustment digitally, as in #3 above, but skip the ADC since the signal starts in the digital domain anyhow.