Although the vast majority of wild mushrooms you'll find in your lawn are non-poisonous, the poisonous ones have no antidote and can cause severe illness or death. Only a qualified mushroom expert should identify the mushrooms growing in your yard, and you must take appropriate precautions to prevent your children and pets from eating them. Even if your dog or child just licks the mushroom, she can become ill if the mushroom is poisonous.
Mushrooms are fungi, spread by spores and have underground networks from which they are growing. While picking them and discarding them may prevent a child or pet from eating the mushroom, to really get rid of them, you have to treat the fungal problem that causes them. Unfortunately, there is no simple way to get rid of mushrooms in your yard.
Your first line of defense is to check your lawn every day for mushrooms. They can spring up overnight so daily vigilance is required. When you find mushrooms, dig them up and discard of them in the trash. Try to pick them before they mature and send out spores. Do not put them on the compost pile. Never kick them or stomp on them to destroy them as this just spreads the spores. Do not run them over with the lawn mower for the same reason.
Keep your lawn cut, dry, and free of debris. Rake up leaves and grass clippings, and scoop up animal droppings. Mushrooms need water and organic matter to grow so water only when necessary and keep your lawn as clean as possible. Water in the morning and deep water to encourage deep root growth. Avoid overfertilizing your lawn as fertilizer encourages the growth of mushrooms.
Talk to your local garden store about fungicides. While these won't totally eliminate the problem, they may help control it to some degree. If a pet or child eats a mushroom from your lawn, seek immediate medical care. Also pick as many of the mushrooms as you can, and take them with you to be identified.