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Rue Mohr has written a great tutorial on how servos work. Even if you already know most of this, it's a great reference on everything from the basic electronics to modifications and optimizations. 

Sample:

Servos are controlled by sending it a variable width pulse (a type of Pulse Width Modulation (PWM)). Important paramiters about the shape of the pulse are the 'centre duration'  and repetition rate. A servo often turns less than 180 degrees on the output shaft over the rated minimum and maximum output pulse lengths.
The centre position of the servo is defined by a pulse width input of 1.5ms high (it should be the shaft position in the middle of its capable movement). The standard pulse width range is 1ms to 2ms, which is often described as having a 180 degree difference in the output shaft, but often does not. (you can go wider on the pulse width changes, for example .9ms to 2.1ms which, depending on the servo, may give you more movement.)
Every time a control pulse is sent to a non-digtital servo, it performs a position 'correction'. The designed correction rate (pulse rate) is 50Hz, or a new pulse every 20ms, more about that later.
So, in summary, the servo expects to see a pulse every 20 milliseconds (ms) and the length of the pulse will determine the output position.
  For example:
   - 1.5ms pulse will make the motor turn to the 90-degree position. 
   - 1 ms pulse moves it to 0 degrees
   - 2 ms pulse will turn the servo to 180 degrees

 

[Via Hackaday]