Nothing. The 'toadstools' or mushrooms are only the fruiting bodies of underground mycelium, a wide ranging root system for the fungus. You only need to worry if the toadstools are occurring near an old, rotting stump and are honey coloured, which could mean honey fungus, or if you have a fairy ring of them in your lawn (about which nothing can be done anyway). If you don't like the look of them, just pull them off at the base. They should disappear after 2-4 weeks anyway, now is the 'flowering' time for the variety you have.
Many plants need fungal mycelium in order to grow properly, but there seems to be a higher incidence of mushrooms or toadstools in gardens after using bark chips.

dosen't moist conditions and rotting animal or plant material cause fungi?

Wildlifebal: One of the roles of fungi is to break down rotting material, and the mycelium are more likely to produce a fruiting body in damp conditions. There was a programme on BBC 4 or 2 recently called 'The Magic of Mushrooms' - worth a look if its still available on the Iplayer, absolutely fascinating.

Just enjoy them. I love them - always thrilled when i get a few (as long as they aren't the two Bamboo mentioned!)Some are really attractive, some edible and all interesting! And of course some are toxic but only if you eat them! (So are hydrangeas but nobody panics about them!)

Fungi growth is usually a good sign as it's normally an indication that your soil is full of good organic matter and nutrients.