  We present results for one-loop matching coefficients between continuum
four-fermion operators, defined in the Naive Dimensional Regularization scheme,
and staggered fermion operators of various types. We calculate diagrams
involving gluon exchange between quark lines, and ``penguin'' diagrams
containing quark loops. For the former we use Landau gauge operators, with and
without $O(a)$ improvement, and including the tadpole improvement suggested by
Lepage and Mackenzie.For the latter we use gauge-invariant operators. Combined
with existing results for two-loop anomalous dimension matrices and one-loop
matching coefficients, our results allow a lattice calculation of the
amplitudes for $K\bar K$ mixing and $K\to\pi\pi$ decays with all corrections of
$O(g^2)$ included. We also discuss the mixing of $\Delta S=1$ operators with
lower dimension operators, and show that, with staggered fermions, only a
single lower dimension operator need be removed by non-perturbative
subtraction.

High Energy Physics - Lattice