The first thing you'll need is a boat, and luckily you have all the gear you need. You can only build on short green grass, so go ahead and click the hammer icon at the bottom of your screen.
First, place the wood. You have 16 pieces, so place them in a 3×5 pattern, then place the last one in the middle at the back of the boat. Place your dragon egg in the middle of the boat, your seat in the front, and the engine in the back, and you should end up with something that looks like the image below.
Make sure the motor is above the wood, not just to the side, or it will fall.
Now tap the hammer icon again to close the build menu, then sit in the seat. Click on the big green button that appears on the left side of the screen, and it's time to navigate. You will descend a small stream into a long river that moves quite fast.
You can't steer the boat unless the engine is on, so click on it to make it spin. Now you can use the A and D keys, or left and right on your gamepad, to steer. You must avoid all rocks and objects in the river. If you bump into them, your boat will be damaged or may even tip over.
A good tip is to have the camera fairly close to the boat. River segments have a black bulkhead between them, and you want the camera to pass it as quickly as possible, or you'll be sailing blind.
After crossing three river segments, a dragon will appear and lift you up into the sky. It will drop you in the treasure room in a castle and you will get the Hidden Treasure Egg as a reward.
