Birds of prey are considered treif. This is because they are likely to have eaten land animals that are unkosher - your average hawk being more likely to eat a mouse than a cow!
Birds, as with land animals, must be killed according to the laws of Shechitah, and may not have died a natural death (that would be fowl!!).
A large percentage of domestic birds are kosher, such as a tame dove, turkey, chicken, tame ducks and tame geese.