Super Mario 64 on N64 - The Tutorial: How to Play Mario 64?

The buttons are those of the N64 version. For the DS, I think replacing Z with L will be enough.

Movement

Walking, Running, Crawling

Walking isn't used often. You just need to not push the stick all the way. If you push it gently, Mario will even take small, discreet steps that let him walk past sleeping plants. Running is the basis of the game; just push the stick in the direction you want. Crawling isn't very useful. Crouch with Z and push the stick.

Swimming

At the surface, press up and "A" to dive. Holding the button, Mario swims calmly, kicking his feet. By pressing repeatedly, Mario does the breaststroke and goes a little faster. Mario is super strong and can get out of the water by jumping. At the surface, hold down and press A. Mario's oxygen goes down underwater and he eventually dies if you leave him without returning to the surface. Note that health points and oxygen are the same gauge in Mario 64. If you have no health left, jump into a body of water, dive for a moment, then return to the surface. Your health points will refill on their own. Be careful, it stops refilling if you leave the water.

Flying

Hanging from the Ceiling

By jumping and holding A, you can hang onto certain ceilings / grates. Essential in some places but honestly a gimmick most of the time.

Jumps

Jump, Double Jump and Triple Jump

The double jump can be done standing still, but you need momentum to do the triple. To do these jumps, you have to jump again as you touch the ground. The second jump is a bit higher (and longer if you move forward); the third is much longer and higher. It's a jump that can take you to distant places (and even more so when combined with a wall kick) but is quite hard to master, because the second jump has to land in just the right spot with enough momentum.

The Backward Somersault

A very safe and very practical jump. To do it, crouch with Z then press "A". It goes in the direction opposite to where Mario is looking. It goes fairly high but not very far. You can lengthen or shorten it by pressing in the appropriate direction. In fact, if you press all the way in the direction Mario is facing, it will be very slightly a forward somersault, because Mario will land a hair in front of where he started. Precise and quick to set up, it's often very handy on moving platforms with an obstacle in the middle.

The Long Jump

As its name suggests, a jump that isn't too high but goes far. It also lets you go faster, so it's ideal for races. Easy to trigger with a minimum of momentum, it's used a lot. While running, press "Z" then "A". It also allows a "bug" called "LBJ", for long back jump, which lets you reach colossal speed in places, allowing "impossible" things.

Pole and Tree Jumps

On poles, there are 2 types of jumps. While climbing, Mario will push off the pole to jump in the direction opposite to where he's facing. He goes quite far, which makes the jump handy because it's easy to adjust. At the very top of the tree, release the up direction and press it again. Mario will then do a handstand. If you jump, he'll shoot very high in the direction of his head (a bit forward while he's doing the handstand). This jump goes really high but not very far. Like the other one, it's quite easy to aim well.

The Side Flip

A very handy jump to master. Changing direction to go in the exact opposite direction of where Mario is facing and jumping immediately lets you make a fairly high jump in the indicated direction. In practice, it's often used for 90° jumps. For example, while running, you turn 90° left, then turn around and jump. It often lets you climb onto a block on your right without wasting time.

The Wall Kick

A jump that will come in handy from time to time. To do it, press A with the right timing to jump again in the opposite direction. With 2 walls facing each other, Mario can climb very high. Roughly speaking, you need an angle under 45° to do it. Incompatible with the long jump and the backward somersault. Very handy with the side flip.

Attacks

The Punch-Punch-Kick Combo

Without moving, press "B" several times. Mario will throw 2 punches then a jump kick. The basic attack (like all attacks) isn't often useful.

The Ground Pound and the Standard Stomp

The standard stomp simply consists of jumping on an enemy to squash it. The ground pound is performed by pressing Z while in the air. Mario will then fall vertically and heavily on his backside. Useful, for example, for pressing switches. The ground pound is used a lot during long falls. Indeed, pressing "Z" interrupts the fall for a brief moment so that Mario changes position. By doing it close to the ground, you can avoid losing many health points from a fall that's too high.

The Dive

An often-used attack because it's done while running by pressing B. As a result, it's often the fastest. Mario dives onto the enemy and eliminates it.

The Sweep Kick

A nice animation for an attack whose usefulness is close to nil. You have to stop, crouch with Z, then press B. Mario will perform a nice sweep halfway between capoeira and a pommel horse routine.

The Jump Kick

The jump kick clearly deserved a place under movement as well, since it also has the advantage of slowing the fall during a jump. At the moment of the kick, Mario halts his fall and can even move, allowing him to lengthen or shorten a jump. It also lets you enter an opening below you. You jump along the wall and, at the level of the cave, you do a kick and steer toward the opening. Very handy in many situations.