[govibe]

ok, so my teacher says that there are two ways to measure polarity: electronegativity or formal charge. He has us draw dipole moments of molecules and we add up all the vectors to see if its polar or not... However, how does having lone pair electrons on the center atom or double bonds affect this polarity?

[Dan]

Could you post a specific example?

Do you mean, "should I include a vectors representing the lone pairs as well as bonds?" ?

If so, no, just draw vectors for the bonds.

[govibe]

how about (IO3)1-? Also another question, since there are three molecules, how do you know where in the model the Oxygen and the lone electrons go?

[Dan]

It sounds like you need to read about VSEPR theory. Search google, wikipedia, or even better look in a textbook.

[nickflamewizard]

for your first question the answer is yes, lone pairs affect polarity:
for example NH3 and NF3- the dipole moment of NH3 is enhanced by  the lone pair while for NF3 the dipole moment is reduced.-draw their structure and the direction of the dipole moment and you will see.
For the second question, yeah, you have to read more about VSEPR.