The physics
A galvanometer is a coil with a needle. Its resistance is G. A small current Ig swings it to full scale.
An ammeter: put a small shunt S side by side with the coil. The coil and the shunt share one voltage.
Ig G = (I − Ig) S
A voltmeter: put a big resistor R in line with the coil. At full scale, Ig flows through both.
V = Ig (G + R)
A real voltmeter takes some current, so it reads a little low. A real ammeter adds a little resistance.