Plastic, polystyrene, wooden boxes and even cardboard lined with strong plastic will suffice. Keep the soil slightly alkaline from a pH 7.5 to 8.5. Sweeten an acid soil with an application of lime. If you desire, prevent a fly problem by watering the mix with pyrethrum prior to sowing. Mushrooms have little trouble with pests as long as the growing area is kept clean.
Mushrooms grow from microscopic spawn.
You may have to send away for spawn from a supplier. The spawn will come attached to a host material. Distribute the spawn evenly over the surface of the compost. Spray finely with water. Cover with sieved compost.