Electric Motors operate through the interaction of a magnetic field and a current carrying conductor.  A current (or flow of charge) moving through a wire creates a magnetic field. Force is developed orthogonal to the direction of current and to the magnetic field. 
     DC motors use a rotating armature to operate with a terminal voltage and constant current.  The armature is a rotating coil of wire with a current running through it.  Motion is produced by the changing or switching of polarities of the voltage and thereby changing the poles of the magnetic field..  This is achieved through the use of a mechanical switch or commutator. 
     The difficulty with motors is that the relative motion between the two magnetic fields will generate a force counter to the direction of motion due to generator action.  This force is known as Counter Electro-Motive Force (CEMF) 
     The image to the right is a basic DC electric motor that uses electro-magnets as the poles.  The Johnson motor uses permanent magnets for the stator or stationary part of the motor. 
     The image to the right is a Johnson DC electric motor.  The Johnson motor uses a stationary permanent magnet and a rotating coil as the armature.  Voltage switching is accomplished by the commutator on one end of the coil.  When the coil is energized a magnetic field is induced in the coil.  This magnetic field reacts with the magnetic field of the permanent  magnet creating a torque.  The torque causes the coil to rotate to align with the magnet.  Inertia causes the coil to continue in the direction of rotation. 
 
In time 1 current is applied to the coil.  The magnetic field develops torque that causes the coil to rotate to align with the S pole at time 2.  As the coil reaches the S pole inertia causes it to pass on to time 3.  In a motor without a commutator the motor slows due to like magnetic forces as it rotates to the N pole. The commutator allows for a cut off in in the coils magnetic field to avoid opposition. Inertia carries the coil around to time 1 and magnetic forces bring it back into alignment as in time 1.
References: 

     Nolan, Peter, J. , Fundamentals of College Physics,Wm. C. Brown Communications, Inc.  Dubuque IA 1995 

     Hanselman, Duane, C. ,  Brushless Permanent-Magnet Motor Design, McGraw-Hill, NY,NY 1994 

     Beaty, H. Wayne & Kirtley, James,L., Jr,  Electric Motor Handbook, McGraw-Hill, NY,NY, 1998 

     Subrahmanyam, Vedam,  Electric Drives Concepts and Applications,  McGraw-Hill, NY,NY, 1994 
 
 

 Related Links: 

 http://freeweb.pdq.net/headstrong/Cat.htm 

 http://www.cocc.edu/~bemerson/classes/202labs/202lab7.html 

 http://ippex.pppl.gov/ippex/module_4/ 

 http://howstuffworks.com/inside-motor.htm 

 http://trc.ucdavis.edu/Coursepages/EXCITES/activities/ccm.html 

 http://fly.hiwaay.net/~palmer/motor.html 

 http://www.mtsu.edu/~pdlee/public2_html/motor1u.html 

 http://www.yale.edu/prgsmart/resources/curricula/electricity.html