How Can an Insulator be Polarized?
Polarization can occur within insulators, but the process occurs in a different manner than it does within a conductor. In a conducting object, electrons are induced into movement across the surface of the conductor from one side of the object to the opposite side. In an insulator, electrons merely redistribute themselves within the atom or molecules nearest the outer surface of the object. To understand the electron redistribution process, it is important to take another brief excursion into the world of atoms, molecules and chemical bonds.
The electrons surrounding the nucleus of an atom are believed to be located in regions of space with specific shapes and sizes. The actual size and shape of these regions is determined by the high-powered mathematical equations common to Quantum Mechanics. Rather than being located a specific distance from the nucleus in a fixed orbit, the electrons are simply thought of as being located in regions often referred to as electron clouds. At any given moment, the electron is likely to be found at some location within the cloud. The electron clouds have varying density; the density of the cloud is considered to be greatest in the portion of the cloud where the electron has the greatest probability of being found at any given moment. And conversely, the electron cloud density is least in the regions where the electron is least likely to be found. In addition to having varying density, these electron clouds are also highly distortable. The presence of neighboring atoms with high electron affinity can distort the electron clouds around atoms. Rather than being located symmetrically about the positive nucleus, the cloud becomes asymmetrically shaped. As such, there is a polarization of the atom as the centers of positive and negative charge are no longer located in the same location. The atom is still a neutral atom; it has just become polarized.
The discussion becomes even more complex (and perhaps too complex for our purposes) when we consider molecules - combination of atoms bonded together. In molecules, atoms are bonded together as protons in one atom attract the electrons in the clouds of another atom. This electrostatic attraction results in a bond between the two atoms. Electrons are shared by the two atoms as they begin to overlap their electron clouds. If the atoms are of different types (for instance, one atom is Hydrogen and the other atom is Oxygen), then the electrons within the clouds of the two atoms are not equally 
It is very common to observe this polarization within molecules. In molecules which have long chains of atoms bonded together, there are often several locations along the chain or near the ends of the chain that have polar bonds. This polarization leaves the molecule with areas which have a concentration of positive charges and other areas with a concentration of negative charges. This principle is utilized in the manufacture of certain commercial products which are used to reduce static cling. The centers of positive and negative charge within the product are drawn to excess charge residing on the clothes. There is a neutralization of the static charge buildup on the clothes, thus reducing their tendency to be attracted to each other. (Other products actually use a different principle. During manufacturing, a thin sheet is soaked in a solution containing positively charged ions. The sheet is tossed into the dryer with the clothes. Being saturated with positive charges, the sheet is capable of attracting excess electrons which are scuffed off of clothes during the drying cycle.)
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