  We give an effective method to determine the multiplier ideals and jumping
numbers associated with a curve singularity $C$ in a smooth surface. We
characterize the multiplier ideals in terms of certain Newton polygons,
generalizing a theorem of Howald, which holds when $C$ is Newton non-degenerate
with respect to some local coordinate system. The method uses toroidal embedded
resolutions and generating sequences of families of valuations, and can be
extended to some classes of higher dimensional hypersurface singularities.
