  This paper builds on our earlier proposal for construction of a positive
inner product for pseudo-Hermitian Hamiltonians and we give several examples to
clarify our method. We show through the example of the harmonic oscillator how
our construction applies equally well to Hermitian Hamiltonians which form a
subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian
matrix Hamiltonians we construct the positive inner product (in the case of
$2\times 2$ matrices for both real as well as complex eigenvalues). When the
quantum mechanical system cannot be diagonalized exactly, our construction can
be carried out perturbatively and we develop the general formalism for such a
perturbative calculation systematically (for real eigenvalues). We illustrate
how this general formalism works out in practice by calculating the inner
product for a couple of ${\cal PT}$ symmetric quantum mechanical theories.
