From StrategyWiki, the free strategy guide and walkthrough wiki

• : Move: Tilt a little to walk and a lot to run.
• :
  • Jump: You can jump in many different ways, depending on how you combine the jump with other actions. Try and find the best jump for every situation.
  • Confirm menu selections
  • Talk to people
  • Swim
  • Activate Pull Stars
  • Grab poles
  • Fire cannons
• :
  • Shoot Star Bits
  • Cancel menu selections
• Shake or :
  • As you progress in the game, you will learn how to spin. Shake or to spin and destroy obstacles or stun enemies. You may also need to spin to activate certain kinds of objects, so try spinning in different places to see what happens.
  • Climb vines
  • Activate Launch Stars
  • Grab and throw objects
  • Skate on ice
  • Use special abilities when transformed
• :
  • Duck
  • Dive in water
  • Drop out of bubbles
• : Move camera
• : Center camera behind Mario
• , : Pause

[edit] Advanced Techniques

• Defeat enemies: You can defeat most enemies by stomping on them with a jump, stunning them with a spin, or shooting them with a Star Bit and then running into them. However, there are some that you can't defeat in these ways. You may need to spin to return an enemy's attacks or an item or mechanism to defeat some enemies.
• Triple Jump: After jumping while you run, press right as you land for three consecutive jumps. On your third jump, you may be able to pull off an especially high jump.
• Spin Jump: Spin in Midair to perform a spin jump. Jumping and then spinning at the peak of your jump allows you to go higher than in a normal jump.
• Backflip: Hold and press to jump backwards. You will leap high into the sky and slightly backward.
• Long Jump: While running, hold and press to jump across long distances.
• Side Somersault: While running, tilt in the opposite direction and press to perform a high jump with a turn.
• Wall Jump: Face a wall and jump toward it, then continue to jump off the wall with good timing by pressing to kick off the wall. In areas where two walls face each other with a small gap, you can use this method to climb to the top.
• Ground Pound: Press in midair. Mario plummets straight down with great force. This can be used to break things, attack enemies, or activate certain switches.
• Homing Stomp: Perform the Spin Jump, and press while spinning. A variation of the Ground Pound that homes in on the nearest enemy, if one is in range.