What measures are conventionally used to "measure" a patient's pain?

Pain scales... There are different ways to measure pain. If the patient is alert/able to speak coherently, etc. , they are asked to rate their pain on a scale of 0-10 where 0 is no pain and 10 is the worst pain you've ever had. If a person is unable to do this, a behavior scale can be used which is based on facial expressions like grimacing.
PAINMETER. "painmeter" is yet to be invented. Pain is a 5th vital sign and it is what you tell anybosdy listening. It is a subjective phenomenon. Good luck.
Many choices. There are many different scales to "measure" pain. A variety of these can be viewed at: http://painconsortium.Nih.Gov/pain_scales/index.Html there are validated scales for most ages and physical states (such as for people who cannot respond to questions). Unfortunately these are mostly subjective, meaning they depend on a person's prior experience with pain.
10 point pain scale. I typically ask patients to rate their pain on a scale from 0 to 10, with 0 being no pain, and 10 being the worst pain that they can imagine.