The gravitational binding energy of the Moon is 120 million, trillion gigajoules. This means that unless you deliver that much energy in one go, the Moon will just crack apart and reform into a sphere. To blow it up, you’ll need to drill mine shafts hundreds of kilometres deep, all over the Moon, and drop a total of 600 billion of the largest nuclear bombs ever built down them.
Any Moon debris that falls on Earth will only have about 1 per cent of the impact energy of a similar-sized asteroid, because of the lower orbital speed. But smaller stones would still be lethal as they would be so numerous. The kinetic energy of the stones would be absorbed by the atmosphere as they burned up, heating the atmosphere until all life was incinerated.
The remaining debris will spread out into rings around the planet. Without the stabilising tidal drag from a single moon, the Earth’s axial tilt will wobble far more than it does now. Over tens of thousands of years, Earth could tilt all the way past 45°, so that most of one hemisphere faces the Sun continuously, and the other is in perpetual darkness.