Dark Cloud will allow you to fish at several locations around the world.  You must have the fishing rod (which is obtained during the event in Alnet's house in Norune Village), and have some bait in inventory.  Bait can be found in chests, stolen or dropped from enemies, or bought in shops.  By catching fish, you earn fishing points, or FP, which can be traded for items and weapons.  These items can be used or, if you prefer, sold.  For instance, you can trade FP for status  removal items, and then sell them at a nearby shop.  You can get Holy Water for 5 FP, and sell it for 60 gold, which can make you quite a bit of money if you are patient.  However, if you don't enjoy fishing, this wouldn't be a recommended method of making money. 

To fish, approach the sign by the body of water, and press X when the ! appears over Toan's head.  You can choose to fish, exchange FP, view your fishing log, or quit fishing.  If you choose to fish, you will get further options.  Press X to cast, □ to change bait, or ○ to quit.  Below these options, it will tell what bait you have equipped.  Make sure that you have the desired bait on your line, and you're ready to cast.  Fish will sometimes nibble at the bait, and if this happens enough, you can lose the bait.  Make sure that you have vibration turned on so you can feel the fish eating at the bait.  Once a fish pulls the bobber below the surface of the water, press X to pull it in.  You will see the fish you caught and how long it is, and that information will be recorded in your fishing log.  You will also learn how many fishing points you have earned.

The following are the locations where you will be able to fish in Dark Cloud: