How to use a captured Pokemon

That means you've probably captured a Shiny Pokemon!

Shiny Pokémon in the games may differ in color from their normal counterparts either very little or very much. Usually the former is the case, with some Pokémon, such as Glaceon or Pichu, having their Shiny form be only a few shades lighter or darker in color, although a majority of the Pokémon that exhibit this are not in their final form of evolution. However, many Pokémon will have a spectacular difference between their normal and Shiny variations; even extremely common Pokémon like Caterpie show a dramatic difference. An evolutionary line is not necessarily guaranteed to have similar alternate colorations, even if their standard colorations remain consistent; both Ponyta and Rapidash have orange flames, but an alternate colored Ponyta has blue flames, while an alternate colored Rapidash has gray flames (with this being the opposite in Generation II). The opposite can also be true, as in the case of Skitty and Delcatty.

Shiny Pokemon have a very low chance of appearing though, so you'll have to be VERY lucky. When you see a shiny pokemon, it will 'sparkle' when it's out of the pokeball and it has a different colour.

When Shiny Pokemon appear on the battlefield, those stars and sparkles accompany him. You can check it yourself by calling out your caught Pokemon to the battlefield.

The chance of an egg being produced is dependent on the Original trainer ID numbers and Species of the pokemon involved.

The day care Man can tell you how likely an egg is going to be generated after each set of 256 steps going on what he says.

Taken from Bulbapedia:

• Same species, Different Original Trainer - "The two seem to get along very well" - 70% (88% with oval charm)
• Same species, Same Original Trainer - "The two seem to get along" - 50% (80% with oval charm)
• Different species, Different Original Trainer - "The two seem to get along" - 50% (80% with oval charm)
• Different species, Same Original Trainer - "The two don't really seem to like each other very much." - 20% (40% with oval charm)
• Different Egg Groups, same gender, or Undiscovered group - The two prefer to play with other Pokémon more than with each other. - 0%

That's all there is to it. It didn't need to change as the generations went on, they've just added more mechanics into it, like IV and nature breeding.