The main thing to look for is your character's sweat when you're trying to catch one. If you're going to catch a standard red one, the sweat will pop up once. If you're going to catch a colored one, two sweats will pop up. If you are going to catch a shiny one, then three sweats will pop up.

If you see one sweat but you want two or three, then all that you have to do is close the app when you see it. Open it back up and then try again. If you want a shiny, then close the app whenever you see less than three sweats, and open it back up, and keep trying to catch that shiny one.

If that cheat gets patched later on, then you can functionally do the same thing without doing the cheat, it will just take longer. Once you catch your Magikarp, go to your pond, scroll up, and then tap the Magikarp to make it jump out of the water. Keep doing this and eventually, it will get murdered by a Pidgeotto. When this happens you'll be sent back to the pond. Repeat as needed.

This can only be done one time, so after that, do all of the training and leagues that you can, and then take the risk every time until you lose your Magikarp. Once you lose it, then you'll be sent right back to the pond to fish. This can be used to grind for experience levels and diamonds as well.

The more levels that you gain, the better your chance of finding a better fishing rod besides the old rod. You'll have to pay a little bit for it, but if you use it, you'll have a better shot at catching a rare or shiny Magikarp.