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Generally, the chance of finding a shiny Pokemon (anywhere, any species) is 1 in over 8000. A method called "chaining" apparently can boost the chances of finding a Shiny Pokemon (only seen in Diamond and Pearl via the Poke-Radar), but the chance is still abysmally low. Other than cheating, there is no sure-fire way to get a shiny.
Chance of that is VERY HIGH. If you already have a Charizard (doesn't have to be shiny), keep it in the day care with another Charizard or Ditto. Make them have millions of babies. Chances are none of them are gonna be shiny, but you could try. The chances are 1 in 10,000.
Shiny Pokemon have a different color than their usual form. They also have a sparkle around them after their call.
Here is the action replay code for a shiny Pokemon in Pokemon Fire Red. 39584B19 D80CC66A, CE71B3D3 1F6A85FB, 198DF179 5413C867, 73ECB8A0 BDD8B251, D5AFFB37 6855972C, 73ECB8A0 BDD8B251. This code has been tested and verified.
First you need to get a growlithe by putting Pokemon fire red GBA into the dual slot of the ds. Then, you do the chaining technique with the pokeradar and get a shiny growlithe. After that, you use a fire stone on growlithe to make it evolve into arcanine.