ASTM E 96 is a standard for the testing of water transfer rate using cup method, in which two methods is elaborated: Desiccant Method and Water Method. The following content is copied from the linked website.
Water Method
Desiccant Method
Operation principle
As shown in above figure (water method as an example), certain amount of water is sealed by a specimen sample in a testing cup; and constant temperature and humidity is maintained in the testing chamber where the testing cup is located. By measuring the weight changes over certain time periodically, the WVTR can be calculated based on the weight change by the following equation.
calculation
The principle and testing procedure can be seen from the linked videos.