  For supersymmetric gauge theories a consistent regularization scheme that
preserves supersymmetry and gauge invariance is not known. In this article we
tackle this problem for supersymmetric QED within the framework of algebraic
renormalization. For practical calculations, a non-invariant regularization
scheme may be used together with counterterms from all power-counting
renormalizable interactions. From the Slavnov--Taylor identity, expressing
gauge invariance, supersymmetry and translational invariance, simple symmetry
conditions are derived that are important in a twofold respect: they establish
exact relations between physical quantities that are valid to all orders, and
they provide a powerful tool for the practical determination of the
counterterms. We perform concrete one-loop calculations in dimensional
regularization, where supersymmetry is spoiled at the regularized level, and
show how the counterterms necessary to restore supersymmetry can be read off
easily. In addition, a specific example is given how the supersymmetry
transformations in one-loop order are modified by non-local terms.
