To get a Migratory Bird Harvest Card for any of those four species, you need to purchase the Migratory Bird Authorization. However, first time requests need to start with the Migratory Bird Hunting Authorization Application at http://wdfw.wa.gov/hunting/permits/migratory/.
You DO NOT need to repeat this process year after year if authorized for a certain species. However, this is not always the case. For example, if you requested authorization for only Snow Goose your first year, but then get an interest to hunt Brant and Sea Duck next year, then you DO need to apply again. This time you would apply for Brant and Sea Duck to obtain those harvest cards.
20th of March, 2015