To determine if H₂S (hydrogen sulfide) is polar or nonpolar, we need to first determine its geometry. This presumes knowing the rules for drawing a correct Lewis structure and you can find more details about Lewis structures here.

Sulfur is the central atom:

 

 

There are 6 + 2 = 8 electrons, and 4 of them are used to make 2 bonds. The remaining four electrons go to the sulfur:

 

 

The central atom has a steric number of 4 – two atoms and two lone pairs. The electron geometry, therefore, is tetrahedral, and the molecular geometry is bent.

 

 

Now, the polarity: The first thing here is to determine if the S-H bond is polar. Depending on the difference in the electronegativity values, covalent bonds can be polar and nonpolar.

 

• If the difference in electronegativity is less than 0.5, the electrons are about equally shared between the two atoms, forming a nonpolar a covalent bond.
• If the difference in electronegativity is between 0.5 and 1.7, we have a polar covalent bond.
• A difference of 1.7 or higher is so large that the electrons are no longer shared, and an ionic bond is formed. Ionic bonds are formed between metals and nonmetals.

Although sulfur is not as electronegative as oxygen, just like in water the dipoles are pointing from the hydrogen to the more electronegative atom, and the overall molecular dipole is pointing up as drawn:

 

 

Overall, we can say that H₂S is slightly polar.

 

Check this 99-question multiple-choice quiz on Geometry and Hybridization:

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