When I teach a horse to back up, I start on the ground. I use split reins and run then through my saddle strings, pulling them forwards. I use a dressage whip in one hand, and stand slightly in front of the horse holding the reins in my left hand. I will point to the chest and say "Back". If horse takes one step back, great! Praise, pats etc. Then we do 2 steps back, no rein pressure etc. If your ground work is solid then it is no big deal. Then I keep using the command BACK and give a slight tug on the reins, enough to have steady even pressure. One step back, rein release. I keep doing this til we get to the point that if I say BACK and apply rein pressure, horse will continue backing up.
Once I am mounted, it is the same. I will just apply rein pressure and give the command BACK, and 9 times out of 10 I've done enough ground work that horse simply accepts and backs up. Once he backs up steady I will start using one leg at a time to move his hindquarter over. One exercise I do is to back up in a circle and a figure 8. I want as much control over my horse's body as possible and this is a great way to do it.
Spent a whole hour today laying in a pasture, waiting for a sparkling vampire to show up. Alas, I woke up and looked over, only to find a mound of horse crap. Sigh.