how does the nervous system cause an increase or decrease in heart rate?

In two main paths:

Sympathetic Nerves

The accelerans, or sympathetic nerves, carry nerve impulses from the medulla oblongata in the brain to the heart. The heart responds by increasing both the rate of contraction and the strength of the contractions. Exercise is one way that this pathway is activated, and can increase your heart rate to up to 180 beats per minute. This will increase the amount of blood pumped by the heart and sent out to exercising muscles.

Activating the Accelerans

When you exercise, your cells use up more oxygen and more carbon dioxide is produced. The increased concentration of carbon dioxide is recorded by special receptors in the aorta and carotid arteries, and this information is passed to the medulla oblongata. Another effect of exercise is that the muscle pump works harder. The muscle pump is the contraction of muscles surrounding your veins, which pushes blood back to the heart. The harder the muscle pump works, the more blood gets sent to the right atrium of the heart. As the atrium stretches to accommodate the extra blood, the stretch receptors in the heart muscle relay the information to the medulla oblongata. These two sources of information will cause the activation of the pathway that will increase your heart rate, thus relieving the full atrium and moving excess carbon dioxide to the lungs for expulsion from the body.

Parasympathetic Nerves

When you are cooling down and no longer need the increased cardiac output required during exercise, pressure receptors in the carotid arteries and the aorta signal the vagus nerves of the parasympathetic nervous system, also originating in the medulla oblongata. They then send the message from the medulla oblongata to the heart that slows your heart rate.

Hormones and the Nervous System

Noradrenaline, or norepinephrine, is a hormone secreted by some sympathetic nerves. It has the ability to cause your arteries to contract, forcing blood through at a faster rate. This hormone has a role in increasing your heart rate and the strength of the beats. Acetylcholine, on the other hand, is a hormone secreted by the vagus nerve to help in the slowing of your heart rate. The sympathetic and parasympathetic nervous systems work together to control your heart rate.