The straight right hand starts with a pivot on the ball of the right foot. Pivot sharply; this puts the weight on the left foot, turns the hips, and then the shoulders. Then, and only then, do you drive the right arm out.
Get somebody to stand- in a boxing stance- facing you with their left hand on your head. You want to throw your straight right under their left arm, concentrating on making sure your right shoulder reaches that left arm before your right fist moves. Remember to rotate your fist so that the punch lands on the two big knuckles.