The best and fastest way to dry the mushrooms is to pre dry them in front of a fan of some kind (like the small fan of the computer power supply...) and then end-dry the now nearly dry mushrooms using some desiccant in a closed container.
The main goal for the drying of a mushroom is to get it to a state where no water is avaiable for competetor molds. They are a few ways of doing this.
Perhaps the best way is to sit them in front of a fan for about 24-48 hours and then transfer them to a desiccant chamber. The desiccant chamber described in the MMGG
looks like this:
They may be dried in a gas oven at low heat (140°F / 60°C or less) for 6-10 hours.
They may also be dried under a heat lamp, on a screen over a heating vent, or in a small electric food dehydrator. However, these ways use heat which can effect the potency of your fruits if too much heat is applied for too long time.
Mushrooms are fully dried when hard to the touch, like crackers, with no spongy feel at all.