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Dipole moments are just vectors that point towards the more electronegative atom. It would help a lot if you knew the shape of the molecule as well. For example, if you wrote H2O as a linear lewis structure, then the vectors would pull with equal and opposite magnitude towards the oxygens on both sides of the H cancelling each other (i.e. non polar), but water is polar. H20 has a bent shape. Almost like an upside down V shape in a sense. The oxygens would pull towards the bottom of the upside down V. They don't exactly opposite each other, and so they don't cancel out. Dipole moments that point toward or away from each other in exactly the same manner (perfectly opposed) will cancel resulting in non polarity. It might get trickier with different molecules, but hope this helps.
To determine polarity, first you should draw the Lewis structure of the compound. Then, you should determine its shape. If the shape is bent or trigonal pyramidal, the compound will be polar. If the shape is linear, trigonal planar, or tetrahedral, it can be polar or nonpolar (assuming there are no lone pairs, or if the lone pairs are evenly spaced so they cancel each other out). For linear, trigonal planar, or tetrahedral shapes, look at the atoms attached to the central atom to determine polarity. If the atoms are all the same, then the compound is nonpolar. If there is more than one kind of atom attached to the central atom, the compound is polar.
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