Monic polynomials of degree 2 over Z/3Z look like x^2 + ax + b with a and b in Z/3Z. There are nine such polynomials since a and b can each be one of the three elements of Z/3Z. By substituting each of the three elements of Z/3Z into each of the nine polynomials for 'x', you can find which of the nine are reducible (have a zero) and which of the nine are irreducible.
