How does a two-stage supercharger like the one found in a Rolls-Royce Merlin work? Does the pilot have any control over it?
Actually yes. A two stage supercharger used a compressor with two or more compression stages, often with an inter cooler between them, driven by a transmission with different gear ratios to control the compressor speed. A schematic of this type of supercharger can be seen here on a Rolls Royce Eagle engine.
On the Supermarine Spitfires powered by the larger Griffon engines the supercharger speed had both a LO and HIGH setting and could either be manually controlled by the pilot or automatically controlled. The HIGH setting was not recommended at lower altitudes to prevent overboosting during operations there.