To answer your questions I suggest you check out how LED manufacturers do this:
"Almost all indicator-type LEDs are rated by their manufacturers in terms of luminous intensity in candelas, rather than light output in lumens. Luminous intensity is a function of the angle from which an LED is seen, so this value should be considered carefully when used to characterize the light output of a particular LED. Two LEDs with the same luminous flux output can have very different peak luminous intensities, if they are designed to produce different beam angles. A narrower beam angle means a higher maximum luminous intensity for the same light output."
http://www.lrc.rpi.edu/programs/NLPIP/lightingAnswers/led/luminousIntensityLightOutput.asp
and:
"Osram Opto Semiconductors follows the recommendations of the International Commission on Illumination (CIE) for luminous intensity measurements of LEDs as described in Publication 127-1997"
http://catalog.osram-os.com/catalogue/catalogue.do?favOid=000000010003381e026800b7&act=showBookmark
As for Standards they all use:
"The Illuminating Engineering Society of North America (IESNA) has developed a comprehensive test method for testing the absolute photometry (i.e., intensity and distribution of light) of solid state lighting (LEDs).
IES LM-79-08 “IES Approved Method for the Electrical and Photometric Measurements of Solid-State Lighting Products,”
http://www.digikey.com/us/en/techzone/lighting/resources/articles/decoding-luminous-intensity-data.html
Here are two detailed descriptions of the procedures used for LED brightness measurements:
http://www.gizmology.net/LEDs.htm
http://www.theledlight.com/technical1.html
Finally, if you could afford it here's a simple LED luminous intensity meter:
http://www.gamma-sci.com/products/intensity-meter/