G'day Captrusty,
The best method is just to dig them out with a spade or trowel, along with say a cupful of the surrounding soil, as soon as they appear. Wear gloves, unless you can positively identify them as an edible/non-toxic species. Backfill the holes with clean soil.
The thing is, they're a bit like an iceberg - they are just the 'fruiting bodies' of a larger dispersed mass of fungal fibres, which runs through the soil. This 'mycelium' is the actual plant.
The purpose of the mushrooms is to distribute the plant's spores, which then grow into further mycelial threads. So if you remove them promptly, the plant will eventually die off. Superphosphate also seems to be toxic to them.
