The chances of getting a shiny are doubled in normal gameplay from 1/8192 to 1/4096. There are also many new ways to encounter shinies while retaining the old methods. The masuda method is probably the second easiest next to chain fishing. I'll discuss all the ways of catching shinies.
1:Pokeradar. The pokeradar has once again made a return to pokemon games and it is simple. you charge it by walking and you go into the patches of grass that are the same. You start a chain if you keep getting the same pokemon over and over again. you continue the chain by either capturing it or fainting it. If you run away, get a different pokemon, turn on your rollerblades, basically do anything other than encounter the previous pokemon---the chain breaks. however, if you get to 40 chains the chances rise to 1/200 and you can keep reseting the pokeradar until you get a shiny patch.
2:Horde. This is a very popular new way of getting shinies. All you do basically do is get a pokemon with sweet scent or if you have honey and keep getting hordes over and over again until you get a shiny.
3:Matsuda Method: Its basically what everyone said, you simply breed 2 pokemon from different regions and you hope for the best. O-powers and having a pokemon with flame body helps this method. This is ideal if you want to control its nature or iv's
4:Chain Fishing. This is also a new way of getting shinies and definitely the easiest. It's basically like pokeradar except that it takes a bit of skill. you have to consecutively reel in pokemon for a chain. the things that break this chain is missing a hook(like basically throwing in a rod but not getting a pokemon either b/c of mistake or simply didn't get a nibble), using wrong key item, moving, or opening any kind of menu. to address the not getting a nibble problem, I strongly suggest getting either a Inkay or Octillery with suction cups that ensures a nibble. I also reccomned not fishing from the shore and also fishing near rocks or anywhere that is closed off. This is the easiest b/c after only 40 chains, the chances go up to 1/200 and stays that way until you break the chain. Don't let this mislead you though b/c it is actually very hard to keep getting every bite. It also took me about 16 tries just to get to 40 and took me to 106 chains before I got my shiny Dragalge. I got my second one at around 167. The things that don't break the chain is running away, capturing it, and fainting it.
5:Friend Safari. The final and last way is very easy but very time consuming. all you basically do is just run around, derping until you get a shiny. This is good for competitive battling as friend safari usually gives the hidden abilities and good natures. It does have an increased shiny rate from the get-go. as soon as you go into one, the chances of getting a shiny goes up to 1/2000.
Hoped this helped you guys! ;)