  We study a problem of systematical evaluation of the quantum corrections for
general 4D supersymmetric K\"ahler sigma models with chiral and antichiral
superpotentials. Using manifestly reparametrization covariant techniques (the
background-quantum splitting and proper-time representation) in the ${\cal
N}=1$ superspace we show how to define unambiguously the one-loop effective
action. We introduce the reparametrization covariant derivatives acting on
superfields and prove that their algebra is analogous to algebra in super
Yang-Mills (SYM) theory. This analogy allows us to use for evaluation of the
effective action in the theory under consideration methods developed for SYM
theory. The divergencies for the model are obtained. It is shown that on
general K\"ahler manifold the one-loop counterterms have the structure of a
supersymmetric WZNW term. Leading finite contribution in covariant derivative
expansion of the one-loop effective action (superfield $a_3$ coefficient) is
calculated.
