How a gyroscope is build on a silicon chip (as in iphone)?

For details search for "iphone gyroscope" o gooogle

It is a vibrating, rather than a rotating, gyroscope. See the article:

http://en.wikipedia.org/..._gyroscope" class='ext_link'>http://en.wikipedia.org/..._gyroscope

The so-called gyroscopes are actually rotational accelerometers using MEMS (Microelectromechanical system) technology.

Imagine a see-saw with springs to hold it in the balanced position.
Linear movement of the whole thing does not unbalance the see-saw - but rotary movement around it's hinge axis will 'leave it behind' due to inertia, with the spring trying to return it to the centre position.

That's how the sensor chip works - it has three see-saw balances created by micromachining as part of the device.

The sensing is done by measuring the capacitance from the see-saw ends to fixed conductive pads - any movement increases the capacitance at one side and decreases it at the other.

This is the chip used in some iphones:
http://www.st.com/web/catalog/sense_power/FM89/SC1288/PF250373

There's a link in that page to the full datasheet for the device.

There are other types of 'solid state' gyro, such as ring laser or fibre optic gyro device. They are far bigger and more expensive than the mems style used in consumer equipment.

These are the type of thing used in aircraft inertial guidance systems.
Info:
http://en.wikipedia.org/..._gyroscope

Another variation is a Coriolis vibratory gyroscope. These work along the lines of sensing the change of angle of a resonating 'pendulum' element - think of the Foucault pendulum experiment, where the pendulum line of motion is static relative to the rotation of the earth.
http://en.wikipedia.org/wiki/Vibrating_structure_gyroscope