One of the tools you will not be given at the start of the game is the fishing rod. This will, amazingly, allow you to fish anywhere there is water, and you can catch all manner of fish and either sell them or use them in various recipes. If you want this tool, you will need to track it down yourself, but thankfully this is pretty easy to do.
Early in the game, a man called Zack will visit your farm and explain that his job is to collect any item you wish to sell from the box beside your field. He then sells it on and gives you the money. You can actually get a fishing rod from Zack if you go and visit him at his house near Mineral Beach.
You can visit Zack between 11:00 am and 4:00 pm, any day of the week except on holidays. Talk with him, and he will tell you he has an old fishing rod for you. The fishing rod works the same way as all other tools when it comes to leveling it and upgrading it. It will level up just from being used, and each level will allow you to upgrade it, as long as you have found the right types of ore in the Spring Mine.
Fishing in the game is straightforward. Find some water, like a pond, lake, or river, and equip your fishing rod in the Tool Pocket. Hit A to throw out the line, then watch the bob carefully. When it moves, hit A again to pull in the fish, and that is it. The higher level fishing rod, the better and bigger fish you can catch, so be sure to keep upgrading it as much as you can.