You can pluck them up, but that's only temporary. I don't think you can really get rid of them. I think some of them are beautiful. I've seen some that light up (lantern of the woods). They pop up in my lawn too after a good rain, but are gone once the sun comes out. I'm not going to worry about them; they are a natural occurrence and indicate healthy & fertile ground.

Not much, as Bathgate says. You can twist off the mushrooms as they arrive and dispose of them, but they are only the fruiting bodies of mycelium contained either in the turf or in the soil beneath. They won't cause any harm (unless they're in a ring shape with discoloured grass in the centre) and it may be that the garden has recently been turfed, and these were in the turf that was supplied, which isn't uncommon. If that's the case, you may find they diminish over the years - certainly, the mushrooms will only appear at certain times and only for a month or so, depending on the variety.

Just mow the lawn. They don't do any harm.

They only last a few days anyway. I like them.