Put this set into words S - {y|y ∈ N or y - 0} .?

The "y - 0" does not mean anything at all. if you mean

S = {y|y ∈ N or y = 0}

then it is read as "S equals the set of all y such that y is a natural number or y equals 0"

"|" in set notation means "such that"
"S - {y|y ∈ N or y < 0}" means
the set, S, minus the set of y such that y is a natural integer or y is less than 0

I'm assuming y - 0 should be y < 0. y - 0 doesn't make sense in this context.

{y|y ...} = set of y values such that y...