What determines a polarity or non polarity? How do we know which atom will be negatively charged?

The polarity of a covalent bond depends on the electronegativity of the two bonding atoms.

If the two bonding atoms are identical, the covalent bond is non-polar. For example, Cl-Cl single bond, O=O double bond and N≡N triple bond are non-polar.

If the two bonding atoms are different, the more electronegative atom would carry negative charge. For example:
• H-Cl single bond is polar., in which the Cl atom carries negative charge because the electronegativity of Cl (3.16) is higher than that of H (2.20).
• N=O double bond is polar, in which the O atom carries negative charge because the electronegativity of O (3.44) is higher than that of N (3.04).
• C≡N triple bond is polar, in which the N atom carries negative charge because the electronegativity of N (3.04) is higher than that of C (2.55).

The more electronegative atom will attract the electrons more strongly and have the partial negative charge. More electronegative means located closer to F in the top right corner of the periodic table.

To have a polar molecule you need two things
1: a difference in electronegativity
2: so non-symmetry in its geometry

If the atoms in a molecule are the same, then there's no EN difference and no polarity. O2 or N2 or Cl2 are nonpolar. (An exception to this rule is ozone, O3.)

If the atoms are different, there is a possibility of polarity.
O is more electronegative than C so carbon monoxide is a polar molecule.
:C:::O: is linear and the O end is slightly negative.

Carbon dioxide, on the other hand, is nonpolar because it is completely symmetrical; there's no way to divide it into a +half and a -half.
::O::C::O:: is linear
the C is slightly + in the center, the O's slightly - on both ends.

Methane, CH4 has a completely symmetrical tetrahedral shape so it is nonpolar. C (EN=2.5) and H (EN=2.2) are also very close in electronegativity so hydrocarbon chains are considered nonpolar.

Ammonia, NH3 is a pyramidal (tripod-like) molecule, N at the apex with 3 H feet if you like. The N is slightly - and the H's at the base are slightly +.

Water, H2O is a V shaped molecule, O at the vertex is slightly - and the H's are slightly +.

Keep periodic relationships in mind as well.
If NH3 is pyramidal and polar, the PH3 will likely be the same since P is under N.

Bonus concept:
You'll probably be asked about H-bonding, a particularly stong kind of polar bond.
H-bonding can occur when H is bonded to N, O, or F.
It is the reason why the boiling point of H2O is significantly higher than H2S and H2Se.
And why the boiling point of NH3 is higher than PH3 and AsH3