Formation is demonstrated of central nervous system anatomic areas as derived from the forebrain (prosencephalon), the midbrain (mesencephalon) and the hindbrain (rhombencephalon). The forebrain and hind brain form 2 divisions while the midbrain remains as one. 
A two step process is involved in neuron development. Neurons differentiate from stem cell precursors, migrate, and develop axons, which is an activity-independent mechanism guided by genetic programs within the neuron. The activity-dependent mechanism takes place once the neurons reach their target area. These processes are complex and involve numerous mediators. 
Neurons travel from their site of origin to their final place within the brain by radial, tangential or mutipolar migration.
The development of the critical central nerve pathways are present at the 6 week embryological stage. Above figure. 
Left: 1. olfactory, 2. optic, 3. oculomotor, 4. trochlear, 5. trigeminal sensory, 6. trigeminal motor, 7. abducens, 8. facial, 9. vestibulocochlear, 10. glossopharyngeal, 11. vagus, 12. cranial accessory, 13. spinal accessory, 14. hypoglossal, 15. cervical I, II, III and IV
The spinal cord is composed of a dorsal (top) sensory portion. Ectoderm induces the development of the roof plate with BMP (Bone morphogenetic proteins). The ventral (bottom) or motor floor plate is induced by the notochord or mesoderm layer. Above figures.  The sensory nerves are primarily afferent in function ( go towards the cord) while the motor nerves are primarily efferent (go away from the cord).. These nerves are functional and fetal movement has been observed as early as 5.5 weeks post fertilization.
Day 20: A demonstration the developing somites, the precursor of which is the mesoderm which is lateral to the neural tube (paraxial). Above figure. 
The somites give rise to the 
2. myotome, and
Somite formation begins about the 3rd week post-fertilization. A total of 52 somites are formed. In the human, the first four somites form the basi-occipital bone of the skull while the next 33 somites form the vertebrae. Above figure. 
The remaining somites then degenerate.
A complex process of somite formation occurs which includes: notch signaling, boundary formation, epithelialization and axis specification. These processes require multiple gene specifications, proteins and other substances. Above figure. 
This is a summary of major embryological events in the formation of the human central nervous system. Note that the distal tip of the cord is different during fetal life compared to the adult distal tip of the spinal cord.
O’Rahilly, R and Muller F. Human Embryology and Teratology. Second Edition. Wiley-Liss. 1996. pages 361-401. http://en.wikipedia.org/wiki/Neural_development_in_humans
Figure: http://en.wikipedia.org/wiki/File:6_week_human_embryo_nervous_system.svg. This is a file from the Wikimedia Commons. Date: May 4, 2010. Source : Own work. Author. Kurzon. Copyright of work released into the public domain.
Figure: http://en.wikipedia.org/wiki/File:Spinal_cord_direv.svg. This is a file from the Wikimedia Commons. This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license. O’Rahilly, R and Muller F. Human Embryology and Teratology. Second Edition. Wiley-Liss. 1996. pages 361-401. O’Rahilly, R and Muller F. Human Embryology and Teratology. Second Edition. Wiley-Liss. 1996. pages 361-401. http://en.wikipedia.org/wiki/Somite.
Figure: http://en.wikipedia.org/wiki/File:Gray20.png. This is a file from the Wikimedia Commons. This image is in the public domain because its copyright has expired. This applies worldwide.