What effects does quantitative easing have on the economy?

It depends on the situation of the "real" economy and the financial markets. The idea is to soften the requirements of collateral of the central bank, by buying for example long terms assets from banks or companies against cash (I'm simplifying of course). So the immediate effect is to increase the balance sheet of the central bank and to put more money (in term of volume) on the markets (increase the liquidity). It is done by central banks when the interest rates are close to zero, when the traditional monetary policy is useless and even more when banks stop lending to each other. So the supposed effect on the "real" economy is the stoppage of the process of deflation, even sometimes create inflation. It lowers as well the value of the currency of the country in which this policy is implemented, leading potentially to an increase of the price of goods bought from abroad.
If the surplus of money is then lend by the banks to companies or people, it is supposed to support investment, consumption, jobs and economic growth. But it depends on the level of confidence in the society/economy of the country. If the people keep saving money, instead of borrowing it will not have the expected effect on the real economy.
On the other hand it can have a negative effect on the financial markets by creating new bubbles on certain classes of assets. There is also a debate around the fact that quantitative easing monetary policies facilitate the increase of inequality in the society, because the richest are more able to access credit easily in a deteriorated economic environment and take advantage of opportunities on the stock or real-estate market at a low cost (by the price of those assets itself and the low interest rates proposed by the banks).

- by Baptiste Mondéhard