When determining whether or not a molecule is polar there are two main things to consider. The first is the electronegativity of the elements that make up the molecule. If there is a significant difference in the electonegativity of the elements then there is an opportunity for a dipole. The other aspect to consider is the shape of the molecule. As long as the dipoles do not cancel each other out then the molecule is most likely polar. This is where it is useful to draw out the structure and determine its shape.
Take, for example, water (H2O). Hydrogen and oxygen have very different values for electronegativity. This can be determined by their location on the periodic table. This means that there will be a dipole, or a significant negative charge on one "side" of the molecule (O) and a significant positive charge on the other "side"(H). Now when you draw the structure for water, you see it has 2 single bonds and 2 lone pairs. From this we could say that the molecule is bent and therefore the dipole moments do not cancel each other out.