The polarity of a bond is determined by the electronegativity of the atoms bonded. If the difference between the electronegativity values for both atoms is small enough to prevent an ionic bond but large enough to be significantly different, a polar covalent bond is formed.
Using the periodic table can help determine the electronegativity of any given element. Certain periodic tables even include the exact or estimated electronegativity value for each known element that does not expire due to a short half-life. Polar bonds are most often seen between nonmetals and are responsible for specific properties, such as water's usefulness as a universal solvent.
Just because a bond is polar does not mean that a molecule will be polar, though. For example, the carbon dioxide molecule is composed of two polar C-O bonds, but is found in a linear shape with carbon in the center. This causes the polar charges to work against each other and cancel out. Alternatively, the water molecule demonstrates a bent shape with the central oxygen atom flexed away from the hydrogen atoms. This allows the polar charges from the O-H bonds to congregate and form slightly negative and positive ends of on the molecule and make it polar.