If you are looking for a golden Magikarp, you are looking for a Shiny Magikarp. Shiny Magikarp are the only golden Magikarp in the game, so I'll assume that's what you mean.
If you are playing any game before X and Y, every Pokemon you encounter (besides a few with a "Shiny lock") have a 1/8192 chance of being Shiny. So your chances of finding that Magikarp aren't so great! Luckily, with techniques such as the Masuda breeding method, you can increase your chances to a more reasonable amount.
However, if you are playing X and Y (as your tags suggest), your chances doubled to 1/4096. You can also use fishing chains and the re-introduced PokeRadar to help find Shiny Pokemon. Your chances are still not very good though, so don't expect to find it very quickly.
Also, another thing I thought I should mention, those gold Shiny Magikarp don't evolve into gold Gyarados, if that's what you're looking for. It'll be red, since Shiny Gyarados is red.