Fishing Rods

There are three different types of Fishing Rods in PokeOne.

Old Rod: The Old Rod is the first fishing rod you typically come across.  You can usually only catch Magikarp with it.
Good Rod: The Good Rod allows you to catch more common and uncommon type Pokemon while fishing.
Super Rod: The Super Rod allows you to catch all the Pokemon that can be found in that area while fishing.

How To Fish: Click on the fishing rod you want to use in your inventory while facing the water. Then you must move 5 steps before clicking it again. You will encounter Pokemon during those 5 steps.

Kanto

The Old Rod can be found in Vermillion City. Talk to the girl in the house to the left of the Pokemon Center.  Then read the book cases.  Then find the old man on the dock and give him one of the quotes.
 
The Good Rod can be found in Fuchsia City by talking to Diego. (The second house to the right from the Pokemon Center with the purple roof.)
 
The Super Rod can be found on Route 12 inside the building that Rorey is standing in front of.  Go inside and talk to Kevin and he will give you the Super Rod.

Johto

The Old Rod can be found in the Pokemon Center on Route 32 by talking to the NPC Jelly.
 
The Good Rod can be found in Olivine City.
 
The Super Rod can be obtained at the Lake of Rage.