For his, her and their, German makes two choices:

1. The owner picks the word: a man → sein; a woman → ihr; several people → ihr (their).
2. The thing owned picks the ending, exactly as with mein: plain for der / das, -e for die and plurals.

Owner	der / das	die / plural
er — his	sein	seine
sie — her	ihr	ihre
sie (plural) — their	ihr	ihre

• Marcos und sein Hund — Marcos and his dog
• Frau Müller und ihr Garten — Frau Müller and her garden
• Herr Müller und seine Zeitung — Herr Müller and his newspaper
• Die Müllers und ihre Söhne — the Müllers and their sons

Sein also covers its for der and das words: das Haus und sein Garten — the house and its garden.