Keep your step light, working through the balls of your feet. You can also lead with the right foot, placing it in front of the left and shifting weight forward and back. Same idea side to side. As you step left with your left foot, shift your weight left and then rock back to the right foot. Vice versa when you step to the right.
Swing dance is very dependent on the rock step.
To perform the basic move of the jitterbug, men take a small step side left and then shift the weight back to the right foot. Cross the left foot behind the right foot and again shift weight forward to the right foot. Small step left, shift right, rock step with the left foot, right. Step, step, rock step, right. The rock step should stay right underneath you and not be a big step back.