On which side of the table are nonmetals located?
The right hand side of the Table as we face it.
The modern Periodic Table illustrates 2 competing elemental properties: (i) nuclear charge; and (ii) shielding by other electrons. As we go across a Period from left to right, nuclear charge increases sequentially, and shielding by other electrons (i.e. those which lie in the same valence shell) is ineffective. As we go down a row in the Table, the nuclear charge is shielded by full valence shells, and the valence electrons are shielded somewhat from the increased nuclear charge.
And thus, towards the left of the Table (always as we face it), the elements tend to be more metallic in character: their valence electrons are loosely held, and these elements tend to be reducing; often the valence electrons are detached from their parent nucleus, and the electrons tend to be delocalized over a matrix of now positively charge ions. It is clear that here we speak of elemental metals, and metallic bonding.
On the other hand, towards the right of the Periodic Table, the increased nuclear charge means that the valence electrons are tighty held, and the elements tend to be more oxidizing: this is certainly the case for elemental oxygen and fluorine. Given the increased nuclear charge, the rightmost elements tend to form discrete molecules in which atom drafts in electron density to complete a valence shell. The result, at least for the first 2 short periods, the rightmost elements tend to be molecular, and non-metallic.