Identifying military ammunition can be much more difficult than identifying civilian ammunition because of the wide variation in bullet identification practices. Different countries throughout World War II --- and manufacturing plants within the same country --- had widely different systems for marking cartridges. In some cases, cartridges themselves may be too corroded to read identifying marks easily, and may need to be gently treated with steel wool or cleaning solutions to remove rust or other grime.
Turn the cartridge carefully, looking for any markings on the case or near the firing pin. World War II ammunition was manufactured to standards very different from civilian ammunition. You should find a short series of letters --- called the bullet's lot numbers --- followed by a series of numbers. These identify the manufacturing plant and year the bullet was made.
Measure the diameter of the bullet. Bullets are often categorised on type based on their measurement; diameter is one of the key identifying measurements. The diameter of a bullet is analagous to the calibre.
Measure the bullet's OAL --- sometimes called COAL --- which is the cartridge's "overall length." While measuring the OAL, identify the separate measurements for the case and the length of the taper.
Write down any other identifying marks found on the case of the cartridge.
Compare this information to available lot number and head stamp information directories, such as those found at cartridgecollectors.org.
Cartridges made in foreign countries may have non-English symbols. When recording identifying marks from the cartridge, try and recreate them as accurately as possible.