How do you use you legs to encourage turning and how do you introduce this to a horse who has no idea?

You must learn first. You can't teach a horse something you don't know how to do either. Get a good instructor with a well schooled horse... although I would consider you not learning this originally as a failing on your first instructor's part. You should be using legs to turn, the rein is there to control flexion and speed. Essentially, the inside leg (the one towards the centre of the circle) is your support beam and stays on the girth. It's what the horse bends around, and keep the horse wide on the circle. The outside leg (the one on the other side of the centre of the circle) pushes the horse around. It's slightly behind the girth to prevent to horse just swinging its hindquarters out.

As for teaching the horse, slowly. You're probably better off getting an experienced rider in to train your horse until you learn yourself. Assuming this horse is used to being turned with just reins, the rider will start by making large associations with leg. So, to go right, the rider will use the right rein, but also put their legs in the correct position. At the start, it will still be entirely turned using the rein. Then when the horse is used to the legs being moved, and associated the legs being where they are with turning, the rider will start using their legs more to turn, and the reins less. Eventually, the horse can start lateral work to really get them used to moving off the leg, before perfecting the circle with legs.
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