Run cancelling is performed by flicking the analog stick down followed by a smash attack.
Wavedashes are performed by air dodging diagonally into the ground which causes the character to slide.
Wavelanding is performed after a character jumps to his/her peak and descends. As the character is approaching the ground the player presses L or R, initiating an air dodge. The ground then stops the air dodge animation and begins a normal wavedash. This is especially useful for moving around platforms quickly and for getting onto the stage quickly.
Text is from ssbwiki