Higher-derivative operators are central elements of any effective field
theory. In supersymmetric theories, these operators include terms with
derivatives in the K\"ahler potential. We develop a toolkit for coupling such
supersymmetric effective field theories to supergravity. We explain how to
write the action for minimal supergravity coupled to chiral superfields with
arbitrary numbers of derivatives and curvature couplings. We discuss two
examples in detail, showing how the component actions agree with the
expectations from the linearized description in terms of a Ferrara-Zumino
multiplet. In a companion paper, we apply the formalism to the effective theory
of inflation.Comment: 26 page