How to tame a nautilus and get nautilus armor in Minecraft
Feed a wild adult nautilus Pufferfish until hearts appear:

The Pufferfish poisons and nauseates whoever eats it, but brewed into an awkward potion it gives water breathing. Fish come from fishing with a rod or from killing fish in the water. All fish work the same; the Cooked Cod page explains them.
This item has no crafting recipe.
Feed a wild adult nautilus Pufferfish until hearts appear:
It is dropped by Pufferfish, Elder Guardian and Guardian. Bought by Villager: Fisherman (Master). Fishing: Fishing Rod.
It is a fish to eat or to use with animals and potions. Brewing: it turns potions into Potion of Water Breathing. Animals that eat it: Nautilus and Wolf.
1 hunger points (0.5 drumsticks) and 0.2 saturation. Effects: Poison (level II · 60 s), Hunger (level III · 15 s) and Nausea (level I · 15 s).
A Balanced Diet (Eat everything that is edible, even if it's not good for you); Fishy Business (Catch a fish).