Breeding can be complicated at first, but I can lay out the basics.
Breeding occurs when two Pokemon that can breed with each other (known as being compatible) are left at the Pokemon Daycare together, where they will produce an egg. Two Pokemon are able to breed with each other if:
- They are not legendary Pokemon, baby Pokemon, Unown, Nidorina or Nidoqueen (any Pokemon that fits this category can breed with Ditto)
- They are of opposite genders (genderless Pokemon can only breed with Ditto)
- They are in the same egg groups (an egg group is a list of Pokemon who can breed with each other if they fit the above two categories)
Obtain the egg by talking to the Daycare Lady. Walk around with it for a bit, and it will hatch. The hatched Pokemon will be the same species as the female but at the bottom of the evolutionary chain- breeding a female Blastoise with a compatible Pokemon will produce a Squirtle. In the case of Ditto, the egg will always be the species of the non-Ditto Pokemon- breeding a male Charizard with Ditto will produce a Charmander.
The main purpose of breeding Pokemon is to pass down moves and IVs from the parent Pokemon to the offspring, as well as obtain baby Pokemon that are otherwise unobtainable in the wild.
And that's it! Not too bad, right? There are more components and exceptions to breeding but this is the main concept of it. You can read about it here for more information about the nitty-grittys of breeding. You can also look it up, as there are other Pokemon websites which may have other information that is not mentioned in the link I gave you.