Just plucking mushrooms from your yard will not necessarily get rid of them since much of it grows below the ground. That being said, it can help. If you let a mushroom mature, spores will be released which can cause more mushrooms to grow. Digging them out and removing their matted roots below the ground can help. Do not throw mushrooms onto a compost pile. Instead, put them into a plastic bag and discard in the garbage. Make sure your ground drains well and has no standing water. Add sand to heavy clay soils. Aerate your lawn. De-thatch it. Remove decaying branches, grass clippings, pet waste and the like. Soapy water can sometimes help to eliminate mushrooms as can nitrogen fertilizers.
As to how to know if a mushroom is poisonous, that is not as easy to answer. Just assume that most of them are poisonous to be on the safe side. If you intend to consume them, read books and consult with experts. There are many edible mushrooms, but there are also many that are poisonous. Some of them look similar. I would rather err on the side of safety. Hope that answers some of your questions.