The C-Stick is the yellow analog stick on the right side of the GameCube controller. In Melee's versus mode, it can be used to perform any smash attack while standing, or any aerial while floating. Smash attacks performed with the C-stick are performed one frame slower than the fastest possible, which has little to no effect on its usefulness. If one presses "Z" (Or any grab button) soon after the player tilts the stick, they can charge the smash attack. It is also possible to charge a smash attack by pressing A when tilting the C-stick, in the same manner the player would if they were using the control stick. The C-stick can also be used to perform aerial attacks, in which case the attack will be performed in the direction the C-stick is tilted. This allows the player to do a back aerial attack without losing their forward momentum. The C-stick can also substitute for the control stick in some instances, as it can be used to air dodge or sidestep from your shield, direct the direction of a tech, and influence directional influence. The C-stick is also notable as the means to perform a DACUS and other advanced techniques.
In Melee's 1 player modes, the C-stick can be used to change the zoom distance of the camera. In order to do this, one must tilt the C-stick up to zoom in and tilt the C-stick down to zoom out. Essentially all players see this as a pointless and disruptive feature, as the camera control cannot do much other than restrict the player's view, and players used to using the C-Stick to attack will find themselves instead taking no action.
In Brawl, the C-stick (And right stick on the classic controller) can be assigned other control behaviors:
In both games, the player can also use the c-stick to change the camera angle on the various menus within the game.
These are some techniques that can be performed with the C-Stick that cannot be performed using the Control Stick and attack button.
 Aerial attacks in opposite directions
Using the C-Stick, the player is able to move through the air in one direction, but input their aerial attack in another direction. For example, a player could move right, but their attack could be inputted so its hitboxes are on the left side.
Smash directional influence can be performed by using both the Control Stick and the C-Stick. By using both joysticks together, the player can SDI at a much farther distance than possible with just one stick.
 Aerials without moving
Using the control stick to perform a forward aerial or back aerial will result in the player moving slightly in the direction inputted. However, the C-Stick does not require a direction on the Control Stick to attack with an aerial, so when used with the C-Stick, the player will not move horizontally. Good for countering approach.