I encountered my first pirated. He sunk my only ship. I quickly built a shipyard and made a new one. That one also didn't stand a chance. So how do I protect my ships against them?

Simple single tower near your port is sufficient for starters. Also, load maximum number of cannons (you have to "mount" cannon by clicking it while having it on board. Otherwise they just sit unused under deck). You can repair your ships.

Another way is to sail with an unarmed ship to the pirates port where you can pay them protection money so they won't attack you for some time. But this doesn't last forever, so think about renewing it from time to time if you don't want or can't fight them yet.

Also you can just whiteflag your ship and surrender. Then the pirate can't attack you, but can take your loaded stuff.
But better loose some goods, then your ship.