All Kamen Rider’s controls are fairly straightforward. D-Pad moves the player on left-right and "inward-outward" axes. B is the Jump button. How long you press the button adjusts how far/high you jump. Y for Light Attacks (press repeatedly for combos). X for a 1-hit heavy attack. It’s used mostly to cap off Y-combos.
A is for Specials. They generally comes in Normal, Directional and Aerial (usually the Rider Kick) varieties. There’s no limit or penalty, so use them as much as you want. You can hold L to guard, and hold A while guarding to perform a Finisher, which hits every enemy on the screen. Finally, R activates special abilities on some Riders. You can check each Rider’s status screen to see which ones apply.
All Kamen Rider is split into "Worlds", and further into "Stages", presented on a map screen. As you scroll through each Stage, beating up enemies, you gain experience and "Coins"; at the end of each Stage, you’ll get a crystal you can break for more of the same stuff. Clear a Stage, and you unlock the next one, plus usually a new Rider. Each Stage also has an optional objective called "Missions". Common objectives include "Clear the stage with this Rider", "Defeat this many enemies with Specials" and "Don’t let your HP go lower than 50%". They can be done in any difficulty, and you only need to complete them once. Complete all Missions in a world to unlock a bonus stage, which means another Rider to unlock and one more Mission.