There are about 8 method to find shiny pokemon available across Gen 6
Here is a video explaining all of them
1) Random encounters. In Gen 6 this is 1/4096. Shiny charm beings this down by a multiple of 3, or about 1/1365.
2) Horde hunting. This is using sweet honey, or the pokemon move sweet sent to attract 5 pokemon to battle at once. The odds are still the same as a random encounter, but your doing it 5 times at once. So your effectively cutting down the time by a factor of 5.
3) soft resetting. This if for legendary pokemon. You just keep encountering it resetting the game until it's shiny. Some legendaries are shiny locked. You soft reset instead of hard resetting because it takes less time. Same odds as random encounters
4) masuda method. Basically breeding two foreign pokemon, foreign to each other, not to your game, changed the odds of hatching a shiny to 1/1365, and down to 1/512 with shiny charm. Most people, like me, who do this want the pokemon to have good IV's, nature and ability. You can give a parent an everstone to always pass down that ability, a destiny knot to the other patent to always pass down 5 random IV's from the parents. I've identical to the parents, but which ones are passed are random. Mothers pass down hidden ability 60% of the time, I think. Father's pass it down 20% if breed with Ditto, I think. Many people use a 6 IV Japanese Ditto for breeding as it satisfied the Masuda method requirements, if breed with a non Japanese partner, and if has good IV's to pass down to offspring. Every 256 steps your pokemon egg has 1 egg Cycle done. Using a pokemon with flamebody makes it so you take down 2 egg cycles instead of 1. Hatching power 3 halves how many steps you need for an egg cycle. So combined hatching an egg is 4 times faster
4) chain fishing. You fish in one spot consecutively. Don't move, and get a bite each time. Exact odds are unown, but it is relatively fast. It helps to have a pokemon with suction cups, or sticky hold, and to fish in an area that is surrounded by rocks, or walls, so you "box in the pokemon". If you get the message no bite, or you reeled in your rod too soon, or too late, or if you move from your spot, turn the game off, the chain ends. Running away from a pokemon, or finding a different pokemon doesn't brake the chain.
5) in pokemon xy there is the friend safari. Each Friend has a type assigned to their friend code. They don't even need to have a pokemon game, but it's better if they do. Each safari has 2 pokemon, and a 3rd if your friend beat the elite 4. Odds here are a flat 1/512. Shiny charm has no effect on it whatsoever. Friend safari pokemon are guaranteed at least 2 perfect 31 IV's.
6) using the xy Radar to chain. It's pretty complicated to explain, at least for me, so you'll want to watch a video of it. To get the radar you need to defeat the elite 4. Then go to the professors lab and talk to one of his researchers on the second floor. The odds to get a shiny increase all the way up until you get to a chain of 40. At this point the odds become 1/512. If you get to a chain of 40, stop encountering pokemon, just keep resetting your chain until you see grass that sparkles and their is your shiny. Shiny charm doesn't change this. Basically you find the pokemon you want to chain and faint or capture it. If you run, or its a different pokemon your chain ends. You'll see grass shake and music start to play. While chaining do not use your Rollerblade or bike. The goal of chaining is to step into the grass that shakes the most violently. If none of them do, take 50 steps and use the radar again until you find grass that shakes a lot. Usually you want to avoid grass that's at the corner. Think of a matrix. Avoid the first and last row of grass and the first and last column of grass. Sometimes the music gets faster. If it does keep resetting your chain until you find sparkling grass. Music lasts like 30 second or a minute I think. Once fast music is done just keep chaining like normal. Again you should watch a video on it. I know how to do it, but I can't get past a chain of 20.
7) Dexnav. This is oras exclusive. It's believed that Using the dexnav gives a similar, if not the same, flat rate that the friend safari gives. Most agree shiny charm does not change it. So chaining doesn't matter for shiny odds. You can chain in order to get pokemon with better IV's, hidden ability, and egg moves. All are shown on the dexnav before you encounter the pokemon.