Without wishing to sound like Ray Mears I do find toadstools quite interesting, and, if you get your identification correct, extremely tasty! However, if you are going to be dining off of your lawn do buy a book on edible mushrooms as the consequences of getting it wrong can be serious.
Toadstools will populate your lawn, usually when the rains start in autumn and if it contains organic material. This is usually a sign of a healthy soil though not always a welcome sight on a fine lawn. Those that are edible (and a few that aren't) will be munched by insects and slugs and some are collected and eaten by squirrels. Otherwise they appear to be left alone by everything including pets and therefore pose no danger.
On occasions a crop of toadstools will grow due to an excessive thatch layer, so when you do see clusters of small mushrooms it is worth inspecting the lawn for thatch. Yet other times you will see them forming a ring known as a ‘fairy ring’ which indicates quite a serious soil condition.
Finally, what do you do with them if you’ve got them?
The first and best thing to do is to remove them to reduce the spores getting into the soil. This will reduce future crops slightly. For the larger ones or if there aren’t too many just go and pick them. If this is going to be too much work either brush them or mow them. Finally, if you like the look of them just leave them and enjoy.