The fishing boat feature unlocks at level 26. Before you reach that level, you will see a lighthouse in disrepair in the water near the daily reward wheel.
Once you reach level 26 you will be given the option to repair the lighthouse for a cost of 9,000 coins. The lighthouse will take 18 hours to repair.
Once your lighthouse is repaired, you will see a fishing boat in the water, moored next to the lighthouse - tapping on the boat will open the fishing menu.
Before you can fish you need to produce tools to fish with, so tap on the lighthouse to open the fishing tool menu. Here you are given a choice of what tools you would like to produce. Hooks cost 50 coins and when used, will catch either fish or seaweed randomly. Using a Glove you can produce a Seaweed Rake or Fish Bait. Producing a Prawn Net requires one Seaweed.
If you specifically want to catch fish (or seaweed) you need a fish lure (or a seaweed rake) - these cost a glove to make. More fishing tools become available as you level up in the game. Tap the Craft button to produce the tool. After 10 minutes your tool will be ready - tap on it to collect.
Now you have your tools, tap on the fishing boat to open the fishing menu. Tap the catch button beneath the tool you wish to use. It will take your fisherman 30 minutes to catch a fish (or snag some seaweed) - after this time, tap on the product to collect.
At first, you can only catch fish or seaweed, other seafood will become available as you level up in the game.