The key to a great side pass is "pushing" never "pulling" the horse into the direction of travel.
To side pass correctly, the horse must move both forehand and hindquarters directly sideways. If moving to the left, the right legs cross over in front of the left legs, both front and back. If moving right, the left legs cross in front of the right fore and hind legs.
To help the horse get started (lateral work is very difficult for a horse) be sure to make an exaggerated weight shift to the side opposite the direction of travel. If you want to move to the right, shift your weight well to the left…then you can push the horse's forehand toward the right with the indirect rein, and you can push the hindquarters to the right with left leg pressure.
While the horse is learning, you'll have to make many small rein and leg cue adjustments. Don't expect a lot of movement when first teaching the side pass. A couple of steps should be greeted with plenty of praise.
Don't seek speed. The side pass should be "correct" before any speed is added. One step at a time is just fine as long as the horse is crossing his feet properly and is not moving forward or backward as he moves sideways.
Taken from the online course Training Performance Horses