Before I get into the particulars on the peripheral nerves I want to give some background info on the structure of nerve cells, and structure of the vertebral column first. Then I'll fit the peripheral nerves into the equation.
I. All About Nerves Neurons are the cells of the nervous system
3 classes of neurons: (Don't forget S.A.M.E.)
1. Sensory (receptor) neurons (afferent)- they carry the impluses from the sense organs to the brain & spinal chord after receptors detect an internal/external change.
2. Motor Neurons (efferent) -they carry impulses from the brain and spinal Cord to the muscles or glands. In response to impulses, Muscles Contract and Glands Secrete.
3. Interneurons - connect sensory and motor neurons and carry impulses between them. They are found entirely within the Central Nervous System.
The structure of a neuron...

(from http://www.enchantedlearning.com/subjects/anatomy/brain/Neuron.shtmlw.enchantedlearning.com/subjects/anatomy/brain/Neuron.shtml)
Helpful hint: Axons send information away from the neuron and the dendrites receive information. Schwann's cells help protect the cell by producing myelin. This allows for an insulated current that is speedy. Now that we have gone over the basics of the neurons here's more about their helper cells...
THE GLIAL CELLS (http://staff.washington.edu/chudler/glia.html) 
Astrocyte(Astroglia) -Star-shaped cells that provide physical and nutritional support for neurons: 1) clean up brain "debris" 2) transport nutrients to neurons; 3) hold neurons in place; 4) digest parts of dead neurons; 5) regulate content of extracellular space
Microglia-Like astrocytes, microglia digest parts of dead neurons.
Oligodendroglia-Provide the insulation (myelin) to neurons in the central nervous system.
Satellite Cells-Physical support to neurons in the peripheral nervous system.
Schwann Cells-Provide the insulation (myelin) to neurons in the peripheral nervous system
II. Organization of the Nervous System:

CNS- "command center' where higher level processing takes place
PNS- nerves that go out to target in the body. they are located outside the brain & spinal vertebrea.
A change in external or internal enviroment is detected and the message is sent to the brain. The brain then sends a signal for muscle movement or gland secretion.

Peripheral Nerves:
Cranial nerves: there are 12 pairs the come directly off the brain
| Nerves | Type | Function |
I Olfactory | sensory | olfaction (smell) |
II Optic | sensory | vision (Contain 38% of all the axons connecting to the brain.) |
III Oculomotor | motor* | eyelid and eyeball muscles |
IV Trochlear | motor* | eyeball mu scles |
V Trigeminal | mixed | Sensory: facial and mouth sensation Motor: chewing |
VI Abducens | motor* | eyeball movement |
VII Facial | mixed | Sensory: taste Motor: facial muscle s and salivary glands |
VIII Auditory | sensory | hearing and balance |
IX Glossopharyngeal | mixed | Sensory: taste Motor: swallowing |
X Vagus | mixed | main nerve of the parasympathetic nervous system (PNS) |
XI Accessory | motor | swallowing; moving head and shoulder |
XII Hypoglossal | motor* | tongue muscles |
SPinal nerves : pairs each with a left & a right coming off the spinal chord
Cervical region 8 pairs
C1 & C2- nerves for the head, face, inner & middle ear, sypathetic nerve system, sinuses, eyes, auditory, nerves.
C3 - C8- neck shoulders, thyroid, tonsils, teeth, outer ear,
nose, mouth, vocal chords
Thoracic Region 12 pairs (pretty much goes to all of the vital organs)
T1 -T12-arms, hands, heart, coronary arteries, esophagus, trachea, lungs, broncial tubes, gallbladder, liver, stomach, pancreas, spleen, kidneys, ureters, adrenal glands, sm intestines
Lumbar Region 5 pairs (pretty much goes to the lower parts)
L1 - L5- lrg intestines, appendix, abdomen, bladder, repro organs, ankles, feet
Sacral Region 5 pairs (goes to the dorsal parts)
S1 - S5- hip area, tail bones area, rectum, anus, buttocks.
Now for how they fit it.....
The spinal chord is surrounded by and protected by the bones of the vertebral column. Like the spinal nerves the vertebral column has the same regions, cervical, thoracic, and sacral and the additional coccyx region (or tailbone)