Always handle the horse evenly on both sides.

This means that while Grooming, Leading, Longing, Saddling, Mounting, Riding, etc., make sure you work the left and right sides evenly. This prevents the horse from becoming one-sided and spooky on the side he's not normally handled on.

For example, if you are most comfortable working on a horse's left side but don't feel comfortable working on his right side, then just do a little bit of work at a time on his right side, and don't push it too much. But do something there! The more practice you and your horse get working with the weaker side, the more natural and easier it becomes.

The horse's performance on the stronger side will also improve, because he won't have to overcompensate as much for the weak side.

Make sure the horse learns to be mounted and dismounted on both sides. Horses easily get one-sided about this and become extremely spooky on the side they are not mounted from. However, be very careful when teaching this to the horse, and go in very small steps.

If the horse spooks while the rider is mounting or dismounting from the weak side, the rider can easily fall and his foot could get caught in the stirrup. To further exacerbate this situation, a rider who is not used to mounting or dismounting from both sides is usually clumsy on the weak side, which makes it ever more dangerous when teaching this to a one-sided horse.

So use common sense. If the horse seems nervous or spooky about the weak side, back off and extend the lesson over several sessions.