Press the and ( and for Classic Controller) together to form a defensive pose that shields you from some enemy attacks.

Press the down to crouch. Crouching while pressing the ( for Classic Controller) lets you pick up weapons and power-up items.

Stand near an opponent and press the ( for Classic Controller) to grab. Press the in a given direction to throw.

Jump and press the up to grab a ledge, then jump again to climb up, or press the left/right to move hand-over-hand.

A number of other regular and character specific techniques are also available. Experiment with combos to find the best ways to control each character.