You can only go fishing in Fisherman's Cove.
You will need some bait, which you can collect from various buildings, or get from clearing the island of trash. Your bait will also replenish automatically over time.
Once you have it, find a place to fish. For instance, let’s take the Fishing Bridge which is near the first location on this island.
Select the bridge and choose the contract that suits you.
Once the contract is selected, you’ll see fish around the bridge. Press on the fish to catch it and send it to the Larder.