A simplified procedure, called the shift-search method, is developed to decode the three possible errors in a (23,12,7) Golay codeword. The algebraic decoding algorithm developed recently by Elia is compared with this algorithm. A computer simulation shows that both algorithms are modular, regular and naturally suitable for either VLSI or software implementation. Both of these algorithms decode efficiently the 1/2-rate (24,12) Golay code for correcting three errors and detecting four errors. The algebraic technique is a slightly faster algorithm in software than the shift-search procedure.