If you’re nervous, it helps to have a calm instructor.
Realize that horses are basically calm grazing animals. They are not out to get you. However, you should be aware that they do want to protect themselves from danger and can react very quickly. With this in mind, think of it as your responsibility to reassure your horse that it is safe in your care. This should help take your mind off you own emotions.
Realize that if you are relaxed (not collapsed) and balanced, gravity is your friend. If you are tense and stiff, you block the stabilizing effect of gravity and tend to bounce. If you relax, a good portion of you weight hangs low on either side of the horse, and it is basically impossible to fall off. There is no need to “hold on”. If you release any unnecessary tension, your muscles will expand allowing the bones of your spine to stack one above another forming natural shock-absorbing curves. With your bones supporting you, your muscles are free to move with the movements of your horse and make the necessary subtle changes to remain in balance.
Think of riding, not as a wrestling match but, as a dance where you and your partner move in harmony. Do everything gracefully.