JAB (second picture above)  -  the most commonly used and the fastest punch in boxing.  It comes from the lead side of your body (whichever foot is forward).  Without moving your legs or turning your waist, throw your leading arm forward in a straight line from your face.  As you punch, rotate fist inward so that palm faces down.  The hand should come back to face as quick as it's thrown out.

CROSS - This punch uses all the muscles in the legs, hips and core.  It's the rear hand thrown with more power.  Fists start at face, travels across chest/shoulder and lands with the rear hips and shoulder forward.  Like the jab, rotate the fist, palm ends facing down as you land the punch.  Return to chin.  You must use the lets and transfer the weight from the back to front simultaneously as you throw the punch.

HOOK - thrown with either hand towards side of opponent.  All the power comes from legs and hips.  To throw a hook, use the fist closer to your opponent, keep fists at side of face and load up your punch by twisting from waist and turning lead shoulder back away from opponent.  Release punch by twisting body forward, turning hips into punch as yo pivot on ball of front foot.  As you punch, simultaneously raise your elbow up as you move your fist away from face and rotate so palm faces you, thumb up.  At point of contact fist should end up a foot from face, with shoulder, elbow and fist all at same height in front of nose.

UPPER CUT (fourth picture above) - This is a devastating knockout punch (used close to an opponent) is one of the most powerful punches in boxing.  It can be thrown with either hand.  To throw a regular uppercut, which uses the fist farther from your opponent, hunch shoulders slightly forward, bend knees and dip down 3 to 4 inches, keep fists close to face.  Begin to drop back fist as you simultaneously swing upward and outward so it leaves the side of face, palm ends up facing you and knuckles pointing to ceiling on the upswing.  Simultaneously transfer bodyweight onto back leg and pivot off the ball of back foot.  As you go, quickly twist hips and shoulders inward.  At point of impact, your elbow should be out and away, in front of body.