A non polar bond occurs when the electrons are equally shared while a polar bond occurs when the electrons are unequally shared due to differences in electronegativity. For example, H2 would be nonpolar because the atoms have the electronegativity. Meanwhile, OH is polar because oxygen is much more negative, so the electrons will be more displaced towards oxygen.
In terms of nonpolar/polar molecules it depnds on the dipole moments of the bonds in the molecule. I'm not sure about molecules being polar and having nonpolar bonds, but I know there are cases where molecules can be nonpolar while having polar bonds. Dr.Lavelle went through an example using trans-Dichloroethene versus cis-Dichloroethene. http://people.uwplatt.edu/~sundin/images/vsprcl2e.gif
Here's an image that might help.
In trans-dichloroethene, the vectors that represent dipole moments cancel each other out, making it a nonpolar molecule despite having polar bonds.
Hope this'll help!