How do you say your nationality in French?

If you are from Australia, you would say:

"Je suis Australienne" (fem.) or "Je suis Australien" (masc.)

"Je suis" ("I am") means "My nationality is" and then you write your nationality.

"your nationality" = "votre nationalité" (fem.)

Tricky nationality capitalization rule:

"Je suis Français" (I am French, capitalized noun, citizen of France)

But "Je suis de nationalité française" (I am of French nationality, uncapitalized because it is an adjective referring to "nationality")