The simplest way (also the most exciting) is to use explosives.
But of course, if you did that in Tokyo or Manhattan or any big city with lots of buildings, it would be...
well, they won't do it.
But there's another way, which is called the first" cut-and-down method" . To do this, the lowest part of the building is cut away. then, they lower the WHOLE BUILDING inch by inch and then repeat the process again. Do this many times and you get a roof of a skyscraper.
There's a video of the process on this site, it's very weird to watch. demolishing a skyscraper (it's in the middle of the sidebar on the right.)Typically, it takes about a week to shorten the building by 1 floor.
But still, it's very silent and safe because all the chaos are happening on the ground, not like the usual procedure that takes it down from the top.