My trainer says with a green horse you want to start out BIG and end up with nothingness.
I more than one way.
The way you help a green horse with balance, and forwardness is almost an exageration of what you would essentially do with a school master to help reinforce what you are asking for. So start of bigger, asking for more forwards, making the bends slightly bendier, exaggerate the movement, almost. After time, take away from it so you as a rider look like you're working less and the horse has to learn to do these things on its own rather than relying on a rider 100% to keep it together all the time.
A favourite excercise of mine is to use changes through half the school, extend those few paces, then really collect when you hit the corners/ direction change.
A lot of people also ride along the outside of the school so much they forget that the horse has to be straight- and this is in any gait. Riding more middle lines, and on the second track will help ensure your horse is straight from you, and you are correctly straightning (sp?) the horse rather than relying on the boards.
Bending is a great tool, and great practise for when you are in the warm up arena and other riders try and cut you up. Making sure you have breaks and the ability to turn and a 2 cent coin is important, IMO. It saves from a lot of accidents from other ignorant riders.
Most importantly though is riding figures correctly. We have a sheet with all school figures laminated at our place for anyone to take a peek at so they know where they should change bends, how they should be ridden, different varities (forward, collected, 10m circles in loops etc) can be ridden. Its alright saying 'I can do 4 loop serpentines' but unless they're ridden correctly then they don't benefit.
Evil excercise 1: 1 Loop Serpentine on the long side working/middle trot, middle of the long side 10m circle to the wall collected trot, contine serpentine working/middle trot.
Evil excercise 2: 4 loop serpentine through the LENGTH of the school, 6-8m circle in each 'bow' or loop. To keep the horse straight and consistant through out takes a lot out of both horse and rider!