How do the central and peripheral nervous system work together?

The Central Nervous System (CNS) and Peripheral Nervous System (PNS) work together in a multitude of ways. The PNS is ultimately the extension of the CNS.

By simple definition, the CNS is located in the spine and in the skull. The PNS in simple definition is everything else. The CNS does the bulk of your processing of the signals being received and the PNS is mostly tasked with providing a place for the inbound signals to start (afferent neuronal signal) or going from the CNS to the rest of the body.

For instance, if you were to touch something extremely hot with your hand, the PNS would send a signal to the spinal cord. From there, the CNS would split the signal.

One signal would go up to your brain, so that you could perceive and recognize that it was hot along with possible recruiting various muscle groups to look at what was hot. The other split signal would be rerouted immediately to the PNS in what is called a "reflex arc". This reflex would travel through the PNS to pull you hand away. The neat part is, the reflex would be completed before your brain received the message that you touched something hot.

So in simple terms again, the PNS is the one who brings the signal in and performs the action. The CNS is the one that interprets and reroutes the signals.