You can EX cancel a lot of normals and special attacks. You do this by hitting the focus attack just after the attack connects. It costs two bars of ex meter to EX cancel. You use this mostly for one of three reasons. To opt out of an attack and make it safe. Ryu wakes up with mp dp, EX cancels right after the first hit and cancels the focus attack by dashing backwards, putting him safely out of reach of most punishes. To juggle or link into ultra. Ryu wakes up with dp, it hits and he cancels, dashes forward and juggles with ultra 1. Or for mixups. Ryu does a block string ending in haduken, EX cancels and dashes forward to throw.
His EX moves don’t really do much more damage, but they do have useful properties. His EX dp is invincible for 16 frames…pretty much as long as it can hit for. About the only use it has is as a get out of jail card. Nothing will beat or trade with it. It’ll always win, unless they’re invincible, too. EX fireball recovers 5 frames faster than a normal fireball and put them into juggle state. So, you can zone with it from just a bit closer and still get off your dp to anti-air. Juggle state allows you to combo to ultra off of it. Easy in the corner, but midscreen you have to EX cancel the fireball or be right next to them when the fireball hits. EX tatsu is his most damaging special, but not really. By itself it does the most dmg, but in most combos it doesn’t scale well. It’s biggest use is that it can juggle. Land it with your opponent cornered and you can juggle into ultra. Can also use it after you land dp xx EX cancel, and don’t have ultra yet.
Use Ryu’s super mostly to punish. It comes out very quickly and travels fast across the screen, allowing you to punish a lot of attacks you normally couldn’t. Dash punches from Rog. Almost any sweep. Blanka ball, whether you block or are hit. It’s very good as a reversal.
As Kelter said, the links are important, too. They’ll add a lot more damage and allow you to hit confirm off a crouching jab, in those situations where you are unsure you can punish, or are pressuring your opponent.
Also, almost no one uses the term EX cancel. Looking around the rest of the forum, you’ll see it refered to as FADC(Focus Attack Dash Cancel). It’s the same thing.