People write entire books about whether quantitative easing does or doesn't work and there's still no agreement!
Quantitative easing doesn't 'give' money to anyone. It simply makes more money available for institutions such as High Street banks to borrow, meaning that they'll be able to lend more. That means that businesses will be able to borrow to invest and individuals will be able to borrow to buy things (both of which should boost economies). So, in the short term, it's well worth considering.
The risk comes when it's left out of control. That results in hyper-inflation and all of the problems that go with it. So, as economic conditions improve, central banks need to gradually claw back the extra money by not continually re-lending it after it's paid back to them. It's getting the exact timing right that can prove to be difficult!