Wind turbines work on a very simple principle: the wind turns the blades, which causes the axis to rotate, which is attached to a generator, which produces DC electricity, which is then converted to AC via an inverter that can then be passed on to power your home.
Wind turbines won't be cost-effective for every home. Much of this depends on how exposed the planned location for your turbine is and how windy the area is. To generate a profitable amount of energy, you'll need a wind speed of around six metres per second.
I've never been close to one, but I believe they aren't silent