How is diastolic pressure measured by a doctor?

Listening carefully. Systolic pressure is the top number and represents the maximal pressure generated by the heart contraction. Diastolic pressure is the pressure during relaxation of the heart. It is measured with a stethoscope as the BP cuff is deflated. As the pressure is brought down in the cuff the first heart beat heard is the systolic pressure. When the heart beat can no longer be heard, that is the diastolic.
Blood pressure cuff. Blood pressure is measured with a cuff - the first number one gets it's the systolic blood pressure, while the second number is the diastolic blood pressure.

Related Questions

Why can't a doctor get my diastolic pressure to decrease?

He can. There are many medications that can reduce the diastolic blood pressure. A combination of several of them might be needed but it should be possible to lower the pressure. Of course, if you are on several medications, you are more likely to get side effects. So the problem is lowering it without intolerable side effects.
They can with. Appropriate lifestyle modification & medication.