Since Spyro has now become an action adventure game rather than a platformer, you're going to need to learn how to fight to play. The first thing you need to know is how to move around. The Left stick controls your movement and the Right stick controls the camera. If you're too close to a wall, you'll only be able to move the camera a small amount. It tries to keep the camera from getting stuck behind walls.
The second thing that you need to know is that you can (and will definitely need to) switch between Cynder and Spyro. To do so, simply press (LT). Switching is relatively seamless, but keep in mind that since one follows the other, you will be a little behind where you were. During fights, they stay pretty close together but if you switch in the middle of battle, you might not be ready for enemies nearby. Both Cynder and Spyro can fly. Simply press (A) a few times to get airborne, then use (A) to flap your wings. You can't always go where you want to, though. I guess the air current is used to block paths that they don't want you to fly over. You can't fly off screen.
To fight, you use the (X) button for a light attack and (Y) for a heavy attack. There are quite a number of combos you can create with these two moves. The game does a very good job of teaching you the fighting techniques in-game. They're also all listed in the instruction booklet. I highly recommend learning how to fight well.
I miss the Spyro games from years ago. The story was more important than the action. The Legend of Spyro: Dawn of the Dragon has beautiful graphics and wonderful voice acting, but it feels short on the story. If you liked the previous one, then you'll probably enjoy this one too. If you're looking for a platformer though, just be aware that Spyro has changed so you won't find that here.