To create a fish pond, you will need the following items:
You can earn 5000 coins by exploring mines, selling crops, or completing tasks for NPCs in the city. The other three are much easier to get: stones can be obtained from the city mine, and seaweed can be obtained by fishing for a certain amount of time throughout the game.
When you have all the resources you need, go to the carpenter's shop. Talk to Robin, after which you can order the Fish Pond. Choose a location for the pond and Robin will start working on it the next morning.