Pokemon Platinum

Not all Pokémon can breed with each other, and some cannot breed at all. In order to breed two Pokémon, the one of them must be male and the other one must be female, or they can be of any gender (even genderless) if one of the parents is Ditto and they must also both belong to the same egg group. Pokémon in the No Eggs group cannot breed. Then you need to take both of them to the "daycare center"; if they are compatible you will get an egg after walking for a while. Pokémon eggs are hatched by walking with the egg in the player's party and the amount of steps depends of the Pokémon species that is inside the egg. The Pokémon that will hatch from the egg will be at level 5 and the same species with it's mother unless one of the following occurs:

If one of the parents is Ditto, then the offspring's species will match with the other parent's species; that means that you cannot hatch a Ditto.
If the mother is a Nidoran♀, then the offspring will either be a Nidoran♀ or Nidoran♂ since they are treated as same species.
If the mother is an Illumise, then the offspring will either be an Illumise or a Volbeat since they are treated as same species.
A Marill/Azumarill's offspring will be a Marill unless one of the parents is holding the item Sea Incense, in that case the baby will be an Azurill.
A Wobbuffet's offspring will be a Wobbuffet unless one of the parents is holding the item Lax Incense, in that case the baby will be a Wynaut.

Baby's Moves

Every baby Pokémon will know some certain moves once hatched. The number of known moves varies (1-4) and depends on its species. They are normally the moves it will know at level 5. However, there is a way to pass down moves from the parents to the offspring allowing the baby Pokémon to know some moves different from the ones it would normally know; this can be done under the following conditions:

Level Up: If the baby Pokémon can learn a move by Level Up and both of its parents know that certain move, then the Pokémon will be born knowing that move.
Machine: If the baby Pokémon can learn a move by using a TM or HM on it and the father knows that move, then the Pokémon will be born knowing that move.
Egg Move: If the baby Pokémon can learn a move through breeding (Egg Move) and the father knows that move, then the Pokémon will be born knowing that move. Each species has its own set of Egg Moves.
Volt Tackle: When breeding for Pichu in Emerald Version, if one of the parents if holding the item Light Ball, then the Pokémon will be born knowing Volt Tackle. Volt Tackle can also be passed down through normal breeding.

Some Pokémon can learn certain moves only from parents that can learn these moves by other Pokémon, we then have to make what is called a breeding chain.

For example Charmander can learn Ancientpower as an Egg Move but no parents in the Monster / Dragon egg groups can learn it as a Level Up move, however Totodile which also learns Ancientpower as an Egg Move belongs to the Monster / Water 1 egg groups, and Relicanth that also belongs to the Water 1 egg group can learn it as a Level Up move. So we need to take a male Relicanth that knows Ancientpower and a female Totodile (or one of its evolutions), we will then make an egg and the newly hatched Totodile will know Ancientpower. Then from the hatched Totodiles we take a male one that knows Ancientpower and have it breed with a female Charmander (or one of it's evolutions). The hatched Charmanders will know Ancientpower.

Moves that can be learn through hereditary replace the preset level 5 moves. However since Pokémon can only know 4 moves, hereditary moves may also replace each other so be careful when you breeding.

Baby's Individual Values

The baby Pokémon will randomly inherit three Individual Values from its parents. So it is good when both parents have decent Individual Values.

However it is impossible to accurately calculate a Pokémon's Individual Values in such a low level but one can hatch a lot of eggs (15+) and then select the Pokémon with the desired stat/nature combination by comparing all the hatched Pokémon. Then the process can be repeated by replacing the parents with the hatched Pokémon until a Pokémon with good stats is produced. Don't forget that while in the Daycare, the Pokémon's level raises which causes them to learn new moves and forget others.

According to Pokéfor²², there is a bug in Ruby/Sapphire and FireRed/LeafGreen versions causing the same stat to be inherited twice and therefore causing the baby to inherit only two Individual Values from its parents.

Baby's Nature

In Emerald Version, if either Ditto or the mother is holding the item Everstone, then the Pokémon's Nature can be passed down. If both a Ditto and a female Pokémon hold an Everstone then the offspring has a 50% chance of getting either parent's nature.

Baby's Ability

If the Pokémon's species has two abilities, then it will randomly know one of them. The parents' abilities have no effect on the baby's ability.

Getting and hatching an egg

The amount of time (steps) that two Pokémon need to make an egg depends on two things: their species and their ID Number. If their species are different and their ID Number is the same they will need more time than if their species are the same and their ID Numbers different.

The amount of time (steps) that an egg needs to hatch depends on the species of the Pokémon inside the egg as already mentioned. Therefore, since riding your bike or playing the game through Pokémon Box increases your speed the amount of time the egg takes to hatch decreases.

In Emerald Version if a Pokémon in your party has the Flame Body (Magby, Magcargo, Magmar, Slugma) or Magma Armor (Camerupt, Magcargo, Slugma) abilities, then the egg will hatch in half the time (steps). Additional Pokémon with such an ability won't have any further effect though.

Advanced breeding information

The chances of getting an egg depend on the parents' species and ID number (both visible and hidden ID numbers). The following cases may occur:

Same species, different ID numbers: The chance of getting an egg is 69,3% (has a value of 70).; The old man in the Daycare will say: "The two seem to get along very well."
Same species, same ID numbers: The chance of getting an egg is 49,5% (has a value of 50).; The old man in the Daycare will say: "The two seem to get along."
Different species, different ID numbers: The chance of getting an egg is 49,5% (has a value of 50).; The old man in the Daycare will say: "The two seem to get along."
Different species, same ID numbers: The chance of getting an egg is 19,8% (has a value of 20).; The old man in the Daycare will say: "The two don't seem to like each other."
Different egg groups: The Pokémon are incompatible and therefore will not make an egg.; The old man in the Daycare will say: "The two prefer to play with other POKéMON than each other."

If the Pokémon are in the Daycare and are compatible, every 256 (0xFF) steps the value mentioned above is compared to a random number generated by the game, if the value is higher than the random number then an egg is produced, if not the same process will be repeated after 256 steps. The higher the value, the better it is.

The random number is between 0 and 65.535 (0xFFFF). Multiplied by 100 and divided by 65.535 (and rounded down by the game as usually) produces a number between 0 and 100, creating a chance of an x in 101 chance of getting an egg.

When the egg is created, the game generates and stores a random number between 1 and 65.535. When you take the egg from the old man in the Daycare another random number (between 0 and 65.535 this time) is generated. Those two numbers combined are used to created the personality value of Pokémon that will hatch from the egg. The personality value determines its Individual Values, gender, nature, ability, shininess, its spots if it's a Spinda or its evolution if it's a Wurmple.

Therefore, once the egg is obtained from the old man, the Pokémon that will hatch from it is determined forever. If you want to hatch a different Pokémon from an egg without having to make multiple eggs for some reason, SAVE the game before getting the egg from the old man.

As a secondary result from the above, it becomes obvious that no matter if a parent is shiny or not, it is completely random if an offspring is shiny or not.