For road handlebars, have somebody measure the distance between the "points" on the front of your shoulders. This is the basis for finding the bar width that allows your arms to be straight while in the drops or on top of the hoods.
Then you have to find out how the handlebar you want is measured.
There's no set standard on how road handlebars are measured. Most are measured from the center of one drop to the center of the other. If the bar you're interested in is measured center to center, simply add 2cm to your shoulder measurement to find the right size--so if the points of your shoulders are 40cm, you want a 42cm handlebar.
Some bars are measured from the outside edge to the outside edge of each side of the bar. For those, you add 4cm--so a 44cm bar would fit 40cm shoulders.
Measure the little pointy places on the front of your shoulders, because the arm radiates from these points. Add 2cm to this measurement for a center-to-center measurement, 4cm for outside-to-outside.
CENTER TO CENTER
Cinelli, Terry, Profile Design, Ritchey, Dimension. Salsa
These brands are measured from center to center--buy the size that's 2cm wider than your shoulder measurement.
OUTSIDE TO OUTSIDE
ITM, TTT, Deda
These are measured outside to outside, so add 4cm to your shoulder measurement to find the right size.
Source: Bicycling Magazine Website