The authors review the algebraic geometry that is needed when one starts with a singular plane curve and wants to define an algebraic-geometric code using the normalization of that curve. Most of this paper is based on an article by the second author and J. J. Risler [Bull. Soc. Math. Fr. 116, No. 2, 231-253 (1988; Zbl 0721.14015)]. The methods are explicitly set forth as algorithms here, which the authors have implemented in AXIOM. Two examples are also presented. Another good source for the algebraic geometry presented here is S. S. Abhyankar’s book “Algebraic Geometry for Scientists and Engineers”, Mathematical Surveys and Monographs 35. Providence, RI: American Mathematical Society (1990; Zbl 0709.14001).