You would be using the Masuda method. You will need at least one Pokemon from the Charmander evolution line, and one Pokemon to breed with it. The two should come from games from different countries*.
- Male Charmeleon from USA + Female Charmeleon from France
- Female Charizard from UK + Ditto from Japan
- Female Charmander from Germany + Male Dragonite from UK
It is to be noted that you will be getting eggs more frequently when breeding two similar species Pokemon (i.e. Charmeleon + Charmeleon but not Charizard + Dragonite), so you might opt for something more like the first example.
This doesn't mean that you will get a shiny quickly; shinies are still rare, but they are easier to come by.
Other things that will help:
- Oval Charm - Increases chances of getting eggs and obtained from Prof. Sycamore for completing KalosDex,
- Shiny Charm - Increases chances of getting shiny Pokemon and obtained from Prof. Sycamore for completing NationalDex.
With the Masuda method, you have 1 in 1,365.3 to get a shiny. If you have a Shiny Charm too, you bring this down to 1 in 1,024 (these figures are from Gen V data, but they are assumed to be the same here, until the figures are confirmed).
And besides this, if your actual aim is a shiny Charizard, it is believed that the Friend Safari has the shiny rate encounter increased. So you might also try to get shiny Charmeleon from a Fire-type Friend Safari with a Charmeleon and the Shiny Charm. I don't know the shiny rate encounter however.
* If it's from the same country but different language, the odds remain unchanged at 1 in 8,192. This is only my speculation based on the fact that in-game traded Pokemon with different languages does not increase the chance of getting shinies through breeding. It's not difficult to get a foreign Pokemon anyway, with GTS.