Push hard from each stride, lean forward from the waist and extend each stride as long as possible and bend the front leg to keep your body as low as possible to the ice. Use crossovers for more speed during turns. Just lift one skate over the other and transfer your weight onto the new inside skate. A great way to practice this is to skate circles in one end of the rink. Be sure to practice going in both directions.
Many people feel scared when learning to skate backward.
Relax it is just as easy as skating forward, you just need to practice it more because you won't skate backward as much as forward in a game. To skate backward you are going to alternate cutting C shaped arches in the ice one at a time. Swing one hip out and create a C arch with one skate, while gliding with the other. Generate some power by thrusting hard off the arch and then transfer your weight and do the same with the other skate. Very simply, that's it.