Finding regular differential $n$-forms on projective varieties.

Question

Do you know if there are known methods, a given projective variety, for finding explicitly the generators of $H^0(X,K_X)$ (when it $\kappa(X)\neq \infty$). I've tried to find them explicitly for surfaces in $\mathbb{P}^3$, but also for the first non-trivial case of q smoot quartic surfaces looks to be difficult. For example how to find the form for the Fermat Quartic $$X_0^4+...X_3^4=0$$