To start the Pirate Quest, go to the Beach and talk to Sharky.

Parrot: Location - Lower Right

Pirate Flag - Location: Lower Left

Gems:

Pirate Hat:

Treasure Chest:

Spyglass:

Compass:

Gold Coins:

Cannon: 

After that go back and talk to Sharky and he will tell you to find Pirate Pete.

  

You then get a reward, called the Beach Quest Pin!

Then go to the dock that's to the right on Sharky on the map. Then you have to get on Pirate Pete's Ship.

Then, click on Pete, and you have completed the quest. And check your costume section of you clothing.

The Reward: