How is blood pressure measured by a doctor or nurse?

Blood pressure cuff. A BP cuff (sphingomanometer) is used over the arm to measure the pressure at which the vessels in your arm collapse with absolutely no blood flowing through them and the lowest pressure at which the lowest flow sounds are heard. These correspond to systolic and diastolic blood pressures.
Sphigmomanometer. Read this wiki for information on the technique: http://en.Wikipedia.Org/wiki/sphygmomanometer.