How can we explicitly calculate the norm of a differential form?

For example let $(X, \omega) $ be a complex manifold such that locally $$ \omega(z) =i\sum_{k,j} h_{k, j} (z) dz_k\wedge d\overline {z_j}\, , $$ and let $\alpha $ be a $(p, q)-$form. How we can calculate the norm of $\alpha $ with respect to the metric $\omega$?