When I was in high school, I once asked one of the players on the ice hockey team how he skated backwards. "It's easy," he said. "All you have to do is do this." Then he pistoned his arms and legs, making him look like an octopus. The fact that he bugged his eyes out made me wonder if he was entirely joking with me.
To start backwards skating in a straight line, first make sure you are very balanced. To go backwards, start skating with one leg doing the pushing (keep the other leg "passive"). When you push with this leg, try to draw a half-circle from the top of the circle to the bottom. This will naturally push you first to the side, then slightly backwards. When you practice this, strive to make your pushes drive into the ice, pushing yourself faster. Then do it for the other leg. Remember: do the half-circle for both legs separately. As you progress, alternate your legs.
It may take many sessions over many weeks or even months for this to become natural. Also, the first few times you attempt these exercises, you'll feel a new kind of "hurt" in your feet. This does go away, and it's only because you're exercising different parts of your legs and feet when you're skating backwards.
I remember hearing the old player's adage that skaters who can skate backwards normally get put on defense. Maybe! I remember watching Paul Kariya, who was a dynamic forward with the Anaheim Ducks, and I swear I never saw him take a backwards stride (though he was certainly one of the fastest skaters I've ever seen "live").
Backwards skating is important for all positions. When you're a forward, and you take your shot on net, one thing you might do is pivot and skate backwards, looking for the rebound on the other side of the slot. Of course, this involves some advanced moves that we'll discuss later.